Kijun Sen Separate WindowThis indicator works the same as a regular Kijun Sen but it is on a separate window to allow for other on chart indicators.
I tend to use this as a filter for when to go long/short.
When it is green, I only take longs. When it is red, I only take shorts. Combine with other indicators of your choice.
在腳本中搜尋"如何用wind搜索股票的发行价和份数"
How To Auto Set Date RangeExample how to automatically set the date range window to be backtested from X days or weeks ago to present. Additional options are also included to manually set the date range or to show entire range available.
Normally when you change chart period it changes the number of days being backtested, which means as you increase the chart period (for example from 5min to 15min), you also increase the number of days traded. So you can not compare apples to apples for which period would yield best performance for your strategy.
By incorporating this code with your own strategy's logic (replacing buy and sell), it will allow you to compare results of different period backtests over the same duration of time.
Date Range: ALL uses entire history.
Date Range: DAYS uses number you set in # Days or Weeks
Date Range: WEEKS uses number you set in # Days or Weeks
Date Range: MANUAL uses manual dates you set in From and To fields
Much gratitude to @pinechrix for suggesting this improvement to me, and to @Gesundheit for pointing me in the right direction on the original example I published previously. Thank you both!
NOTICE: This is an example script and not meant to be used as an actual strategy. By using this script or any portion thereof, you acknowledge that you have read and understood that this is for research purposes only and I am not responsible for any financial losses you may incur by using this script!
How To Set Backtest Date RangeExample how to select and set date range window to be backtested. Normally when you change chart period it changes the number of days being backtested which means as you increas the chart period (for example from 5min to 15min) you also increase the number of days traded, so you can not compare apples to apples for which period would yield best returns for your strategy. Now you can. Incorporate this code replacing buy and sell with your strategy, then simply input the From and To dates in Format -> Inputs, and then change the chart period to view updated results.
NOTE: There is a limit in backtesting to 2000 orders, so please be aware of this when setting your date ranges. If you set your range too high, you may be exceeding this limit on some periods and not on others, so this would yield incorrect comparison of returns per period. If you see in your backtesting results that you are nearing this limit for one of your periods you are testing, then reduce the date range to a smaller number of days.
Enjoy!
(Thanks to @Gesundheit "Adeel" for pointing me in the right direction on this!)
Shadow TradingThis is a very simple script that identify daily candles with big tails and enter the market if the lower or the higher price of the same candle is violated... this is the idea behind I hope you will find it usefull ;)
Swing Hull/rsi/EMA StrategyA Swing trading strategy that use a combination of indicators, Hull average to get the trend direction, ema and rsi do the rest, use it are your own risk expecially at the end of any hull trend
Past Performance Does Not Guarantee Future Results
[Pandora] Laguerre Ultimate Explorations MulticatorIt's time to begin demonstrations differentiating the difference between known and actual feasibility beyond imagination... Welcome to my algorithmic twilight zone .
INTRODUCTION:
Hot off my press, I present this Laguerre multicator employing PSv6.0, originally formulated by John Ehlers for TASC - July 2025 Traders Tips. Basically I transcended Ehlers' notions of transversal filtration with an overhaul of his Laguerre design with my "what if" Pandora notions included. Striving beyond John Ehlers' original intended design. This action packed indicator is a radically revamped version of his original filter using novel techniques. My aim was to explore whether providing even more enhanced responsiveness and lesser lag is possible and how. Presented here is my mind warping results to witness.
EHLERS' LAGUERRE EXPLAINED:
First and foremost, the concept of Ehlers' Laguerre-izing method deserves a comprehensive deep dive. Ehlers' Laguerre filter design, as it functions originally, begins with his Ultimate Smoother (US) followed by a gang of four LERP (jargon for Linear intERPolation) filters. Following a myriad of cascading LERPs is a window-like FIR filter tapped into the LERP delay values to provide extra smoothness via the output.
On a side note, damping factor controlled LERP filters resemble EMAs indeed, but aren't exactly "periodic" filters that would have a period/length parameter and their subsequent calculations. I won't go into fine-grained relationship details, but EMA and LERP are indeed related in approach, being cousins of similar pedigree.
EXAMINING LAGUERRE:
I focused firstly on US initialization obstacles at Pine's bar_index==0 with nz() in abundance. The next primary notion of intrigue I mostly wondered about was, why are there four LERP elements instead of fewer or more. Why not three or why not two LERPs, etc... 1-4-6-4-1, I remember seeing those coefficients before in high pass filters.
Gathering my thoughts from that highpass knowledge base, I devised other tapped configuration modes to inspect their behavior out of curiosity. Eureka! There is actually more to Laguerre than Ehlers' mind provided, now that I had formulated additional modes. Each mode exhibits it's own lag/smoothness characteristics better than the quad LERPed version. I narrowed it down to a total of 5 modes for exploration. Mode 0 is just the raw US by itself.
ANALYZING FILTER BEHAVIORS:
Which option might be possibly superior, and how may I determine that? Fortunately, I have a custom-built analyzer allowing me to thoroughly examine transient responses across multiple periodicities simultaneously, providing remarkable visual insights.
While Ehlers has meagerly touched upon presenting general frequency responses in his books, I have excelled far beyond that. This robust filter analysis capability enables me to observe finer aspects hidden to others, ultimately leading to the deprecation of numerous existing filters. Not only this, but inventing entirely new species of filtration whether lowpass, highpass, or bandpass is already possible with a thorough comprehensive evaluation.
Revealing what's quirky with each filter and having the ability to discover what filters may be lacking in performance, is one of it's implications. I'm just going to explain this: For example US has a little too much overshoot to my liking, along with nonconformant cutoff frequency compliance with the period parameter. Perhaps Ehlers should inspect US coefficients a bit closer... I hope stating this is not received in an ill manner, as it's not my intention here.
What this technically eludes to is that UltimateSmoother can be further improved, analogous to my Laguerre alterations described above. I will also state Laguerre can indeed be reformulated to an even greater extent concerning group delay, from what I have already discussed. Another exciting time though... More investigative research is warranted.
LAGUERRE CONCLUSIONS:
After analyzing Laguerre's frequency compliance, transient responses, amplitudes, lag, symmetry across periodicities, noise rejection, and smoothness... I favor mode 3 for a multitude of reasons over the mode 4 configuration, but mostly superb smoothing with less lag, AND I also appreciated mode 1 & 2 for it's lower lag performance options.
Each mode and lag (phase shift) damping value has it's own unique characteristics at extremes, yet they demonstrate additional finesse in it's new hybrid form without adding too much more complexity. This multicator has a bunch of Laguerre filters in the overlay chart over many periodicities so you can easily witness it's differing periodic symmetries on an input signal while adjusting lag and mode.
LAGUERRE OSCILLATOR:
The oscillator is integrated into the laguerreMulti() function for the intention of posterity only. I performed no evaluation on it, only providing the code in Pine. That wasn't part of my intended exploration adventure, as I'm more TREND oriented for the time being, focusing my efforts there.
Market analysis has two primary aspects in my observations, one cyclic while the other is trending dynamics... There's endless oscillators, but my expectations for trend analysis seems a little lesser explored in my opinion, hence my laborious trend endeavors. Ehlers provided both indicator facets this time around, and I hope you find the filtration aspect more intriguing after absorption of this reading.
FUNCTION MODULES EXPLAINED:
The Ultimate Smoother is an advanced IIR lowpass smoothing filter intended to minimize noise in time series data with minimal group delay, similar to a traditional biquad filter. This calculation helps to create a smoother version of the original signal without the distortions of short-term fluctuations and with minimal lag, adjustable by period.
The Modified Laguerre Lowpass Filter (MLLF) enhances the functionality of US by introducing a Laguerre mode parameter along side the lag parameter to refine control over the amount of additional smoothing/lag applied to the signal. By tethering US with this LERPed lag mechanism, MLLF achieves an effective balance between responsiveness and smoothness, allowing for customizable lag adjustments via multiple inputs. This filter ends with selecting from a choice of weighted averages derived from a gang of up to four cascading LERP calculations, resulting with smoother representations of the data.
The Laguerre Oscillator is a momentum-like indicator derived from the output of US and a singular LERPed lowpass filter. It calculates the difference between the US data and Laguerre filter data, normalizing it by the root mean square (RMS). This quasi-normalization technique helps to assess the intensity of the momentum on any timeframe within an expected bound range centered around 0.0. When the Laguerre Oscillator is positive, it suggests that the smoothed data is trending upward, while a negative value indicates a downward trend. Adjustability is controlled with period, lag, Laguerre mode, and RMS period.
Goertzel Browser [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Browser indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
█ Brief Overview of the Goertzel Browser
The Goertzel Browser is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
3. Project the composite wave into the future, providing a potential roadmap for upcoming price movements.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the past and dotted lines for the future projections. The color of the lines indicates whether the wave is increasing or decreasing.
5. Displaying cycle information: The indicator provides a table that displays detailed information about the detected cycles, including their rank, period, Bartel's test results, amplitude, and phase.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements and their potential future trajectory, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast and WindowSizeFuture: These inputs define the window size for past and future projections of the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
UseCycleList: This boolean input determines whether a user-defined list of cycles should be used for constructing the composite wave. If set to false, the top N cycles will be used.
Cycle1, Cycle2, Cycle3, Cycle4, and Cycle5: These inputs define the user-defined list of cycles when 'UseCycleList' is set to true. If using a user-defined list, each of these inputs represents the period of a specific cycle to include in the composite wave.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Browser Code
The Goertzel Browser code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Browser function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past and future window sizes (WindowSizePast, WindowSizeFuture), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, goeWorkFuture, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Browser algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Browser code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Browser code calculates the waveform of the significant cycles for both past and future time windows. The past and future windows are defined by the WindowSizePast and WindowSizeFuture parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in matrices:
The calculated waveforms for each cycle are stored in two matrices - goeWorkPast and goeWorkFuture. These matrices hold the waveforms for the past and future time windows, respectively. Each row in the matrices represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Browser function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Browser code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Browser's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for both past and future time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast and WindowSizeFuture:
The WindowSizePast and WindowSizeFuture are updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
Two matrices, goeWorkPast and goeWorkFuture, are initialized to store the Goertzel results for past and future time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for past and future waveforms:
Three arrays, epgoertzel, goertzel, and goertzelFuture, are initialized to store the endpoint Goertzel, non-endpoint Goertzel, and future Goertzel projections, respectively.
Calculating composite waveform for past bars (goertzel array):
The past composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Calculating composite waveform for future bars (goertzelFuture array):
The future composite waveform is calculated in a similar way as the past composite waveform.
Drawing past composite waveform (pvlines):
The past composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
Drawing future composite waveform (fvlines):
The future composite waveform is drawn on the chart using dotted lines. The color of the lines is determined by the direction of the waveform (fuchsia for upward, yellow for downward).
Displaying cycle information in a table (table3):
A table is created to display the cycle information, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
Filling the table with cycle information:
The indicator iterates through the detected cycles and retrieves the relevant information (period, amplitude, phase, and Bartel value) from the corresponding arrays. It then fills the table with this information, displaying the values up to six decimal places.
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms for both past and future time windows and visualizes them on the chart using colored lines. Additionally, it displays detailed cycle information in a table, including the rank, period, Bartel value, amplitude (or cycle strength), and phase of each detected cycle.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles and potential future impact. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
No guarantee of future performance: While the script can provide insights into past cycles and potential future trends, it is important to remember that past performance does not guarantee future results. Market conditions can change, and relying solely on the script's predictions without considering other factors may lead to poor trading decisions.
Limited applicability: The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Browser indicator can be interpreted by analyzing the plotted lines and the table presented alongside them. The indicator plots two lines: past and future composite waves. The past composite wave represents the composite wave of the past price data, and the future composite wave represents the projected composite wave for the next period.
The past composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend. On the other hand, the future composite wave line is a dotted line with fuchsia indicating a bullish trend and yellow indicating a bearish trend.
The table presented alongside the indicator shows the top cycles with their corresponding rank, period, Bartels, amplitude or cycle strength, and phase. The amplitude is a measure of the strength of the cycle, while the phase is the position of the cycle within the data series.
Interpreting the Goertzel Browser indicator involves identifying the trend of the past and future composite wave lines and matching them with the corresponding bullish or bearish color. Additionally, traders can identify the top cycles with the highest amplitude or cycle strength and utilize them in conjunction with other technical indicators and fundamental analysis for trading decisions.
This indicator is considered a repainting indicator because the value of the indicator is calculated based on the past price data. As new price data becomes available, the indicator's value is recalculated, potentially causing the indicator's past values to change. This can create a false impression of the indicator's performance, as it may appear to have provided a profitable trading signal in the past when, in fact, that signal did not exist at the time.
The Goertzel indicator is also non-endpointed, meaning that it is not calculated up to the current bar or candle. Instead, it uses a fixed amount of historical data to calculate its values, which can make it difficult to use for real-time trading decisions. For example, if the indicator uses 100 bars of historical data to make its calculations, it cannot provide a signal until the current bar has closed and become part of the historical data. This can result in missed trading opportunities or delayed signals.
█ Conclusion
The Goertzel Browser indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Browser indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Browser indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
The first term represents the deviation of the data from the trend.
The second term represents the smoothness of the trend.
λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
Goertzel Cycle Composite Wave [Loxx]As the financial markets become increasingly complex and data-driven, traders and analysts must leverage powerful tools to gain insights and make informed decisions. One such tool is the Goertzel Cycle Composite Wave indicator, a sophisticated technical analysis indicator that helps identify cyclical patterns in financial data. This powerful tool is capable of detecting cyclical patterns in financial data, helping traders to make better predictions and optimize their trading strategies. With its unique combination of mathematical algorithms and advanced charting capabilities, this indicator has the potential to revolutionize the way we approach financial modeling and trading.
*** To decrease the load time of this indicator, only XX many bars back will render to the chart. You can control this value with the setting "Number of Bars to Render". This doesn't have anything to do with repainting or the indicator being endpointed***
█ Brief Overview of the Goertzel Cycle Composite Wave
The Goertzel Cycle Composite Wave is a sophisticated technical analysis tool that utilizes the Goertzel algorithm to analyze and visualize cyclical components within a financial time series. By identifying these cycles and their characteristics, the indicator aims to provide valuable insights into the market's underlying price movements, which could potentially be used for making informed trading decisions.
The Goertzel Cycle Composite Wave is considered a non-repainting and endpointed indicator. This means that once a value has been calculated for a specific bar, that value will not change in subsequent bars, and the indicator is designed to have a clear start and end point. This is an important characteristic for indicators used in technical analysis, as it allows traders to make informed decisions based on historical data without the risk of hindsight bias or future changes in the indicator's values. This means traders can use this indicator trading purposes.
The repainting version of this indicator with forecasting, cycle selection/elimination options, and data output table can be found here:
Goertzel Browser
The primary purpose of this indicator is to:
1. Detect and analyze the dominant cycles present in the price data.
2. Reconstruct and visualize the composite wave based on the detected cycles.
To achieve this, the indicator performs several tasks:
1. Detrending the price data: The indicator preprocesses the price data using various detrending techniques, such as Hodrick-Prescott filters, zero-lag moving averages, and linear regression, to remove the underlying trend and focus on the cyclical components.
2. Applying the Goertzel algorithm: The indicator applies the Goertzel algorithm to the detrended price data, identifying the dominant cycles and their characteristics, such as amplitude, phase, and cycle strength.
3. Constructing the composite wave: The indicator reconstructs the composite wave by combining the detected cycles, either by using a user-defined list of cycles or by selecting the top N cycles based on their amplitude or cycle strength.
4. Visualizing the composite wave: The indicator plots the composite wave, using solid lines for the cycles. The color of the lines indicates whether the wave is increasing or decreasing.
This indicator is a powerful tool that employs the Goertzel algorithm to analyze and visualize the cyclical components within a financial time series. By providing insights into the underlying price movements, the indicator aims to assist traders in making more informed decisions.
█ What is the Goertzel Algorithm?
The Goertzel algorithm, named after Gerald Goertzel, is a digital signal processing technique that is used to efficiently compute individual terms of the Discrete Fourier Transform (DFT). It was first introduced in 1958, and since then, it has found various applications in the fields of engineering, mathematics, and physics.
The Goertzel algorithm is primarily used to detect specific frequency components within a digital signal, making it particularly useful in applications where only a few frequency components are of interest. The algorithm is computationally efficient, as it requires fewer calculations than the Fast Fourier Transform (FFT) when detecting a small number of frequency components. This efficiency makes the Goertzel algorithm a popular choice in applications such as:
1. Telecommunications: The Goertzel algorithm is used for decoding Dual-Tone Multi-Frequency (DTMF) signals, which are the tones generated when pressing buttons on a telephone keypad. By identifying specific frequency components, the algorithm can accurately determine which button has been pressed.
2. Audio processing: The algorithm can be used to detect specific pitches or harmonics in an audio signal, making it useful in applications like pitch detection and tuning musical instruments.
3. Vibration analysis: In the field of mechanical engineering, the Goertzel algorithm can be applied to analyze vibrations in rotating machinery, helping to identify faulty components or signs of wear.
4. Power system analysis: The algorithm can be used to measure harmonic content in power systems, allowing engineers to assess power quality and detect potential issues.
The Goertzel algorithm is used in these applications because it offers several advantages over other methods, such as the FFT:
1. Computational efficiency: The Goertzel algorithm requires fewer calculations when detecting a small number of frequency components, making it more computationally efficient than the FFT in these cases.
2. Real-time analysis: The algorithm can be implemented in a streaming fashion, allowing for real-time analysis of signals, which is crucial in applications like telecommunications and audio processing.
3. Memory efficiency: The Goertzel algorithm requires less memory than the FFT, as it only computes the frequency components of interest.
4. Precision: The algorithm is less susceptible to numerical errors compared to the FFT, ensuring more accurate results in applications where precision is essential.
The Goertzel algorithm is an efficient digital signal processing technique that is primarily used to detect specific frequency components within a signal. Its computational efficiency, real-time capabilities, and precision make it an attractive choice for various applications, including telecommunications, audio processing, vibration analysis, and power system analysis. The algorithm has been widely adopted since its introduction in 1958 and continues to be an essential tool in the fields of engineering, mathematics, and physics.
█ Goertzel Algorithm in Quantitative Finance: In-Depth Analysis and Applications
The Goertzel algorithm, initially designed for signal processing in telecommunications, has gained significant traction in the financial industry due to its efficient frequency detection capabilities. In quantitative finance, the Goertzel algorithm has been utilized for uncovering hidden market cycles, developing data-driven trading strategies, and optimizing risk management. This section delves deeper into the applications of the Goertzel algorithm in finance, particularly within the context of quantitative trading and analysis.
Unveiling Hidden Market Cycles:
Market cycles are prevalent in financial markets and arise from various factors, such as economic conditions, investor psychology, and market participant behavior. The Goertzel algorithm's ability to detect and isolate specific frequencies in price data helps trader analysts identify hidden market cycles that may otherwise go unnoticed. By examining the amplitude, phase, and periodicity of each cycle, traders can better understand the underlying market structure and dynamics, enabling them to develop more informed and effective trading strategies.
Developing Quantitative Trading Strategies:
The Goertzel algorithm's versatility allows traders to incorporate its insights into a wide range of trading strategies. By identifying the dominant market cycles in a financial instrument's price data, traders can create data-driven strategies that capitalize on the cyclical nature of markets.
For instance, a trader may develop a mean-reversion strategy that takes advantage of the identified cycles. By establishing positions when the price deviates from the predicted cycle, the trader can profit from the subsequent reversion to the cycle's mean. Similarly, a momentum-based strategy could be designed to exploit the persistence of a dominant cycle by entering positions that align with the cycle's direction.
Enhancing Risk Management:
The Goertzel algorithm plays a vital role in risk management for quantitative strategies. By analyzing the cyclical components of a financial instrument's price data, traders can gain insights into the potential risks associated with their trading strategies.
By monitoring the amplitude and phase of dominant cycles, a trader can detect changes in market dynamics that may pose risks to their positions. For example, a sudden increase in amplitude may indicate heightened volatility, prompting the trader to adjust position sizing or employ hedging techniques to protect their portfolio. Additionally, changes in phase alignment could signal a potential shift in market sentiment, necessitating adjustments to the trading strategy.
Expanding Quantitative Toolkits:
Traders can augment the Goertzel algorithm's insights by combining it with other quantitative techniques, creating a more comprehensive and sophisticated analysis framework. For example, machine learning algorithms, such as neural networks or support vector machines, could be trained on features extracted from the Goertzel algorithm to predict future price movements more accurately.
Furthermore, the Goertzel algorithm can be integrated with other technical analysis tools, such as moving averages or oscillators, to enhance their effectiveness. By applying these tools to the identified cycles, traders can generate more robust and reliable trading signals.
The Goertzel algorithm offers invaluable benefits to quantitative finance practitioners by uncovering hidden market cycles, aiding in the development of data-driven trading strategies, and improving risk management. By leveraging the insights provided by the Goertzel algorithm and integrating it with other quantitative techniques, traders can gain a deeper understanding of market dynamics and devise more effective trading strategies.
█ Indicator Inputs
src: This is the source data for the analysis, typically the closing price of the financial instrument.
detrendornot: This input determines the method used for detrending the source data. Detrending is the process of removing the underlying trend from the data to focus on the cyclical components.
The available options are:
hpsmthdt: Detrend using Hodrick-Prescott filter centered moving average.
zlagsmthdt: Detrend using zero-lag moving average centered moving average.
logZlagRegression: Detrend using logarithmic zero-lag linear regression.
hpsmth: Detrend using Hodrick-Prescott filter.
zlagsmth: Detrend using zero-lag moving average.
DT_HPper1 and DT_HPper2: These inputs define the period range for the Hodrick-Prescott filter centered moving average when detrendornot is set to hpsmthdt.
DT_ZLper1 and DT_ZLper2: These inputs define the period range for the zero-lag moving average centered moving average when detrendornot is set to zlagsmthdt.
DT_RegZLsmoothPer: This input defines the period for the zero-lag moving average used in logarithmic zero-lag linear regression when detrendornot is set to logZlagRegression.
HPsmoothPer: This input defines the period for the Hodrick-Prescott filter when detrendornot is set to hpsmth.
ZLMAsmoothPer: This input defines the period for the zero-lag moving average when detrendornot is set to zlagsmth.
MaxPer: This input sets the maximum period for the Goertzel algorithm to search for cycles.
squaredAmp: This boolean input determines whether the amplitude should be squared in the Goertzel algorithm.
useAddition: This boolean input determines whether the Goertzel algorithm should use addition for combining the cycles.
useCosine: This boolean input determines whether the Goertzel algorithm should use cosine waves instead of sine waves.
UseCycleStrength: This boolean input determines whether the Goertzel algorithm should compute the cycle strength, which is a normalized measure of the cycle's amplitude.
WindowSizePast: These inputs define the window size for the composite wave.
FilterBartels: This boolean input determines whether Bartel's test should be applied to filter out non-significant cycles.
BartNoCycles: This input sets the number of cycles to be used in Bartel's test.
BartSmoothPer: This input sets the period for the moving average used in Bartel's test.
BartSigLimit: This input sets the significance limit for Bartel's test, below which cycles are considered insignificant.
SortBartels: This boolean input determines whether the cycles should be sorted by their Bartel's test results.
StartAtCycle: This input determines the starting index for selecting the top N cycles when UseCycleList is set to false. This allows you to skip a certain number of cycles from the top before selecting the desired number of cycles.
UseTopCycles: This input sets the number of top cycles to use for constructing the composite wave when UseCycleList is set to false. The cycles are ranked based on their amplitudes or cycle strengths, depending on the UseCycleStrength input.
SubtractNoise: This boolean input determines whether to subtract the noise (remaining cycles) from the composite wave. If set to true, the composite wave will only include the top N cycles specified by UseTopCycles.
█ Exploring Auxiliary Functions
The following functions demonstrate advanced techniques for analyzing financial markets, including zero-lag moving averages, Bartels probability, detrending, and Hodrick-Prescott filtering. This section examines each function in detail, explaining their purpose, methodology, and applications in finance. We will examine how each function contributes to the overall performance and effectiveness of the indicator and how they work together to create a powerful analytical tool.
Zero-Lag Moving Average:
The zero-lag moving average function is designed to minimize the lag typically associated with moving averages. This is achieved through a two-step weighted linear regression process that emphasizes more recent data points. The function calculates a linearly weighted moving average (LWMA) on the input data and then applies another LWMA on the result. By doing this, the function creates a moving average that closely follows the price action, reducing the lag and improving the responsiveness of the indicator.
The zero-lag moving average function is used in the indicator to provide a responsive, low-lag smoothing of the input data. This function helps reduce the noise and fluctuations in the data, making it easier to identify and analyze underlying trends and patterns. By minimizing the lag associated with traditional moving averages, this function allows the indicator to react more quickly to changes in market conditions, providing timely signals and improving the overall effectiveness of the indicator.
Bartels Probability:
The Bartels probability function calculates the probability of a given cycle being significant in a time series. It uses a mathematical test called the Bartels test to assess the significance of cycles detected in the data. The function calculates coefficients for each detected cycle and computes an average amplitude and an expected amplitude. By comparing these values, the Bartels probability is derived, indicating the likelihood of a cycle's significance. This information can help in identifying and analyzing dominant cycles in financial markets.
The Bartels probability function is incorporated into the indicator to assess the significance of detected cycles in the input data. By calculating the Bartels probability for each cycle, the indicator can prioritize the most significant cycles and focus on the market dynamics that are most relevant to the current trading environment. This function enhances the indicator's ability to identify dominant market cycles, improving its predictive power and aiding in the development of effective trading strategies.
Detrend Logarithmic Zero-Lag Regression:
The detrend logarithmic zero-lag regression function is used for detrending data while minimizing lag. It combines a zero-lag moving average with a linear regression detrending method. The function first calculates the zero-lag moving average of the logarithm of input data and then applies a linear regression to remove the trend. By detrending the data, the function isolates the cyclical components, making it easier to analyze and interpret the underlying market dynamics.
The detrend logarithmic zero-lag regression function is used in the indicator to isolate the cyclical components of the input data. By detrending the data, the function enables the indicator to focus on the cyclical movements in the market, making it easier to analyze and interpret market dynamics. This function is essential for identifying cyclical patterns and understanding the interactions between different market cycles, which can inform trading decisions and enhance overall market understanding.
Bartels Cycle Significance Test:
The Bartels cycle significance test is a function that combines the Bartels probability function and the detrend logarithmic zero-lag regression function to assess the significance of detected cycles. The function calculates the Bartels probability for each cycle and stores the results in an array. By analyzing the probability values, traders and analysts can identify the most significant cycles in the data, which can be used to develop trading strategies and improve market understanding.
The Bartels cycle significance test function is integrated into the indicator to provide a comprehensive analysis of the significance of detected cycles. By combining the Bartels probability function and the detrend logarithmic zero-lag regression function, this test evaluates the significance of each cycle and stores the results in an array. The indicator can then use this information to prioritize the most significant cycles and focus on the most relevant market dynamics. This function enhances the indicator's ability to identify and analyze dominant market cycles, providing valuable insights for trading and market analysis.
Hodrick-Prescott Filter:
The Hodrick-Prescott filter is a popular technique used to separate the trend and cyclical components of a time series. The function applies a smoothing parameter to the input data and calculates a smoothed series using a two-sided filter. This smoothed series represents the trend component, which can be subtracted from the original data to obtain the cyclical component. The Hodrick-Prescott filter is commonly used in economics and finance to analyze economic data and financial market trends.
The Hodrick-Prescott filter is incorporated into the indicator to separate the trend and cyclical components of the input data. By applying the filter to the data, the indicator can isolate the trend component, which can be used to analyze long-term market trends and inform trading decisions. Additionally, the cyclical component can be used to identify shorter-term market dynamics and provide insights into potential trading opportunities. The inclusion of the Hodrick-Prescott filter adds another layer of analysis to the indicator, making it more versatile and comprehensive.
Detrending Options: Detrend Centered Moving Average:
The detrend centered moving average function provides different detrending methods, including the Hodrick-Prescott filter and the zero-lag moving average, based on the selected detrending method. The function calculates two sets of smoothed values using the chosen method and subtracts one set from the other to obtain a detrended series. By offering multiple detrending options, this function allows traders and analysts to select the most appropriate method for their specific needs and preferences.
The detrend centered moving average function is integrated into the indicator to provide users with multiple detrending options, including the Hodrick-Prescott filter and the zero-lag moving average. By offering multiple detrending methods, the indicator allows users to customize the analysis to their specific needs and preferences, enhancing the indicator's overall utility and adaptability. This function ensures that the indicator can cater to a wide range of trading styles and objectives, making it a valuable tool for a diverse group of market participants.
The auxiliary functions functions discussed in this section demonstrate the power and versatility of mathematical techniques in analyzing financial markets. By understanding and implementing these functions, traders and analysts can gain valuable insights into market dynamics, improve their trading strategies, and make more informed decisions. The combination of zero-lag moving averages, Bartels probability, detrending methods, and the Hodrick-Prescott filter provides a comprehensive toolkit for analyzing and interpreting financial data. The integration of advanced functions in a financial indicator creates a powerful and versatile analytical tool that can provide valuable insights into financial markets. By combining the zero-lag moving average,
█ In-Depth Analysis of the Goertzel Cycle Composite Wave Code
The Goertzel Cycle Composite Wave code is an implementation of the Goertzel Algorithm, an efficient technique to perform spectral analysis on a signal. The code is designed to detect and analyze dominant cycles within a given financial market data set. This section will provide an extremely detailed explanation of the code, its structure, functions, and intended purpose.
Function signature and input parameters:
The Goertzel Cycle Composite Wave function accepts numerous input parameters for customization, including source data (src), the current bar (forBar), sample size (samplesize), period (per), squared amplitude flag (squaredAmp), addition flag (useAddition), cosine flag (useCosine), cycle strength flag (UseCycleStrength), past sizes (WindowSizePast), Bartels filter flag (FilterBartels), Bartels-related parameters (BartNoCycles, BartSmoothPer, BartSigLimit), sorting flag (SortBartels), and output buffers (goeWorkPast, cyclebuffer, amplitudebuffer, phasebuffer, cycleBartelsBuffer).
Initializing variables and arrays:
The code initializes several float arrays (goeWork1, goeWork2, goeWork3, goeWork4) with the same length as twice the period (2 * per). These arrays store intermediate results during the execution of the algorithm.
Preprocessing input data:
The input data (src) undergoes preprocessing to remove linear trends. This step enhances the algorithm's ability to focus on cyclical components in the data. The linear trend is calculated by finding the slope between the first and last values of the input data within the sample.
Iterative calculation of Goertzel coefficients:
The core of the Goertzel Cycle Composite Wave algorithm lies in the iterative calculation of Goertzel coefficients for each frequency bin. These coefficients represent the spectral content of the input data at different frequencies. The code iterates through the range of frequencies, calculating the Goertzel coefficients using a nested loop structure.
Cycle strength computation:
The code calculates the cycle strength based on the Goertzel coefficients. This is an optional step, controlled by the UseCycleStrength flag. The cycle strength provides information on the relative influence of each cycle on the data per bar, considering both amplitude and cycle length. The algorithm computes the cycle strength either by squaring the amplitude (controlled by squaredAmp flag) or using the actual amplitude values.
Phase calculation:
The Goertzel Cycle Composite Wave code computes the phase of each cycle, which represents the position of the cycle within the input data. The phase is calculated using the arctangent function (math.atan) based on the ratio of the imaginary and real components of the Goertzel coefficients.
Peak detection and cycle extraction:
The algorithm performs peak detection on the computed amplitudes or cycle strengths to identify dominant cycles. It stores the detected cycles in the cyclebuffer array, along with their corresponding amplitudes and phases in the amplitudebuffer and phasebuffer arrays, respectively.
Sorting cycles by amplitude or cycle strength:
The code sorts the detected cycles based on their amplitude or cycle strength in descending order. This allows the algorithm to prioritize cycles with the most significant impact on the input data.
Bartels cycle significance test:
If the FilterBartels flag is set, the code performs a Bartels cycle significance test on the detected cycles. This test determines the statistical significance of each cycle and filters out the insignificant cycles. The significant cycles are stored in the cycleBartelsBuffer array. If the SortBartels flag is set, the code sorts the significant cycles based on their Bartels significance values.
Waveform calculation:
The Goertzel Cycle Composite Wave code calculates the waveform of the significant cycles for specified time windows. The windows are defined by the WindowSizePast parameters, respectively. The algorithm uses either cosine or sine functions (controlled by the useCosine flag) to calculate the waveforms for each cycle. The useAddition flag determines whether the waveforms should be added or subtracted.
Storing waveforms in a matrix:
The calculated waveforms for the cycle is stored in the matrix - goeWorkPast. This matrix holds the waveforms for the specified time windows. Each row in the matrix represents a time window position, and each column corresponds to a cycle.
Returning the number of cycles:
The Goertzel Cycle Composite Wave function returns the total number of detected cycles (number_of_cycles) after processing the input data. This information can be used to further analyze the results or to visualize the detected cycles.
The Goertzel Cycle Composite Wave code is a comprehensive implementation of the Goertzel Algorithm, specifically designed for detecting and analyzing dominant cycles within financial market data. The code offers a high level of customization, allowing users to fine-tune the algorithm based on their specific needs. The Goertzel Cycle Composite Wave's combination of preprocessing, iterative calculations, cycle extraction, sorting, significance testing, and waveform calculation makes it a powerful tool for understanding cyclical components in financial data.
█ Generating and Visualizing Composite Waveform
The indicator calculates and visualizes the composite waveform for specified time windows based on the detected cycles. Here's a detailed explanation of this process:
Updating WindowSizePast:
The WindowSizePast is updated to ensure they are at least twice the MaxPer (maximum period).
Initializing matrices and arrays:
The matrix goeWorkPast is initialized to store the Goertzel results for specified time windows. Multiple arrays are also initialized to store cycle, amplitude, phase, and Bartels information.
Preparing the source data (srcVal) array:
The source data is copied into an array, srcVal, and detrended using one of the selected methods (hpsmthdt, zlagsmthdt, logZlagRegression, hpsmth, or zlagsmth).
Goertzel function call:
The Goertzel function is called to analyze the detrended source data and extract cycle information. The output, number_of_cycles, contains the number of detected cycles.
Initializing arrays for waveforms:
The goertzel array is initialized to store the endpoint Goertzel.
Calculating composite waveform (goertzel array):
The composite waveform is calculated by summing the selected cycles (either from the user-defined cycle list or the top cycles) and optionally subtracting the noise component.
Drawing composite waveform (pvlines):
The composite waveform is drawn on the chart using solid lines. The color of the lines is determined by the direction of the waveform (green for upward, red for downward).
To summarize, this indicator generates a composite waveform based on the detected cycles in the financial data. It calculates the composite waveforms and visualizes them on the chart using colored lines.
█ Enhancing the Goertzel Algorithm-Based Script for Financial Modeling and Trading
The Goertzel algorithm-based script for detecting dominant cycles in financial data is a powerful tool for financial modeling and trading. It provides valuable insights into the past behavior of these cycles. However, as with any algorithm, there is always room for improvement. This section discusses potential enhancements to the existing script to make it even more robust and versatile for financial modeling, general trading, advanced trading, and high-frequency finance trading.
Enhancements for Financial Modeling
Data preprocessing: One way to improve the script's performance for financial modeling is to introduce more advanced data preprocessing techniques. This could include removing outliers, handling missing data, and normalizing the data to ensure consistent and accurate results.
Additional detrending and smoothing methods: Incorporating more sophisticated detrending and smoothing techniques, such as wavelet transform or empirical mode decomposition, can help improve the script's ability to accurately identify cycles and trends in the data.
Machine learning integration: Integrating machine learning techniques, such as artificial neural networks or support vector machines, can help enhance the script's predictive capabilities, leading to more accurate financial models.
Enhancements for General and Advanced Trading
Customizable indicator integration: Allowing users to integrate their own technical indicators can help improve the script's effectiveness for both general and advanced trading. By enabling the combination of the dominant cycle information with other technical analysis tools, traders can develop more comprehensive trading strategies.
Risk management and position sizing: Incorporating risk management and position sizing functionality into the script can help traders better manage their trades and control potential losses. This can be achieved by calculating the optimal position size based on the user's risk tolerance and account size.
Multi-timeframe analysis: Enhancing the script to perform multi-timeframe analysis can provide traders with a more holistic view of market trends and cycles. By identifying dominant cycles on different timeframes, traders can gain insights into the potential confluence of cycles and make better-informed trading decisions.
Enhancements for High-Frequency Finance Trading
Algorithm optimization: To ensure the script's suitability for high-frequency finance trading, optimizing the algorithm for faster execution is crucial. This can be achieved by employing efficient data structures and refining the calculation methods to minimize computational complexity.
Real-time data streaming: Integrating real-time data streaming capabilities into the script can help high-frequency traders react to market changes more quickly. By continuously updating the cycle information based on real-time market data, traders can adapt their strategies accordingly and capitalize on short-term market fluctuations.
Order execution and trade management: To fully leverage the script's capabilities for high-frequency trading, implementing functionality for automated order execution and trade management is essential. This can include features such as stop-loss and take-profit orders, trailing stops, and automated trade exit strategies.
While the existing Goertzel algorithm-based script is a valuable tool for detecting dominant cycles in financial data, there are several potential enhancements that can make it even more powerful for financial modeling, general trading, advanced trading, and high-frequency finance trading. By incorporating these improvements, the script can become a more versatile and effective tool for traders and financial analysts alike.
█ Understanding the Limitations of the Goertzel Algorithm
While the Goertzel algorithm-based script for detecting dominant cycles in financial data provides valuable insights, it is important to be aware of its limitations and drawbacks. Some of the key drawbacks of this indicator are:
Lagging nature:
As with many other technical indicators, the Goertzel algorithm-based script can suffer from lagging effects, meaning that it may not immediately react to real-time market changes. This lag can lead to late entries and exits, potentially resulting in reduced profitability or increased losses.
Parameter sensitivity:
The performance of the script can be sensitive to the chosen parameters, such as the detrending methods, smoothing techniques, and cycle detection settings. Improper parameter selection may lead to inaccurate cycle detection or increased false signals, which can negatively impact trading performance.
Complexity:
The Goertzel algorithm itself is relatively complex, making it difficult for novice traders or those unfamiliar with the concept of cycle analysis to fully understand and effectively utilize the script. This complexity can also make it challenging to optimize the script for specific trading styles or market conditions.
Overfitting risk:
As with any data-driven approach, there is a risk of overfitting when using the Goertzel algorithm-based script. Overfitting occurs when a model becomes too specific to the historical data it was trained on, leading to poor performance on new, unseen data. This can result in misleading signals and reduced trading performance.
Limited applicability:
The Goertzel algorithm-based script may not be suitable for all markets, trading styles, or timeframes. Its effectiveness in detecting cycles may be limited in certain market conditions, such as during periods of extreme volatility or low liquidity.
While the Goertzel algorithm-based script offers valuable insights into dominant cycles in financial data, it is essential to consider its drawbacks and limitations when incorporating it into a trading strategy. Traders should always use the script in conjunction with other technical and fundamental analysis tools, as well as proper risk management, to make well-informed trading decisions.
█ Interpreting Results
The Goertzel Cycle Composite Wave indicator can be interpreted by analyzing the plotted lines. The indicator plots two lines: composite waves. The composite wave represents the composite wave of the price data.
The composite wave line displays a solid line, with green indicating a bullish trend and red indicating a bearish trend.
Interpreting the Goertzel Cycle Composite Wave indicator involves identifying the trend of the composite wave lines and matching them with the corresponding bullish or bearish color.
█ Conclusion
The Goertzel Cycle Composite Wave indicator is a powerful tool for identifying and analyzing cyclical patterns in financial markets. Its ability to detect multiple cycles of varying frequencies and strengths make it a valuable addition to any trader's technical analysis toolkit. However, it is important to keep in mind that the Goertzel Cycle Composite Wave indicator should be used in conjunction with other technical analysis tools and fundamental analysis to achieve the best results. With continued refinement and development, the Goertzel Cycle Composite Wave indicator has the potential to become a highly effective tool for financial modeling, general trading, advanced trading, and high-frequency finance trading. Its accuracy and versatility make it a promising candidate for further research and development.
█ Footnotes
What is the Bartels Test for Cycle Significance?
The Bartels Cycle Significance Test is a statistical method that determines whether the peaks and troughs of a time series are statistically significant. The test is named after its inventor, George Bartels, who developed it in the mid-20th century.
The Bartels test is designed to analyze the cyclical components of a time series, which can help traders and analysts identify trends and cycles in financial markets. The test calculates a Bartels statistic, which measures the degree of non-randomness or autocorrelation in the time series.
The Bartels statistic is calculated by first splitting the time series into two halves and calculating the range of the peaks and troughs in each half. The test then compares these ranges using a t-test, which measures the significance of the difference between the two ranges.
If the Bartels statistic is greater than a critical value, it indicates that the peaks and troughs in the time series are non-random and that there is a significant cyclical component to the data. Conversely, if the Bartels statistic is less than the critical value, it suggests that the peaks and troughs are random and that there is no significant cyclical component.
The Bartels Cycle Significance Test is particularly useful in financial analysis because it can help traders and analysts identify significant cycles in asset prices, which can in turn inform investment decisions. However, it is important to note that the test is not perfect and can produce false signals in certain situations, particularly in noisy or volatile markets. Therefore, it is always recommended to use the test in conjunction with other technical and fundamental indicators to confirm trends and cycles.
Deep-dive into the Hodrick-Prescott Fitler
The Hodrick-Prescott (HP) filter is a statistical tool used in economics and finance to separate a time series into two components: a trend component and a cyclical component. It is a powerful tool for identifying long-term trends in economic and financial data and is widely used by economists, central banks, and financial institutions around the world.
The HP filter was first introduced in the 1990s by economists Robert Hodrick and Edward Prescott. It is a simple, two-parameter filter that separates a time series into a trend component and a cyclical component. The trend component represents the long-term behavior of the data, while the cyclical component captures the shorter-term fluctuations around the trend.
The HP filter works by minimizing the following objective function:
Minimize: (Sum of Squared Deviations) + λ (Sum of Squared Second Differences)
Where:
1. The first term represents the deviation of the data from the trend.
2. The second term represents the smoothness of the trend.
3. λ is a smoothing parameter that determines the degree of smoothness of the trend.
The smoothing parameter λ is typically set to a value between 100 and 1600, depending on the frequency of the data. Higher values of λ lead to a smoother trend, while lower values lead to a more volatile trend.
The HP filter has several advantages over other smoothing techniques. It is a non-parametric method, meaning that it does not make any assumptions about the underlying distribution of the data. It also allows for easy comparison of trends across different time series and can be used with data of any frequency.
However, the HP filter also has some limitations. It assumes that the trend is a smooth function, which may not be the case in some situations. It can also be sensitive to changes in the smoothing parameter λ, which may result in different trends for the same data. Additionally, the filter may produce unrealistic trends for very short time series.
Despite these limitations, the HP filter remains a valuable tool for analyzing economic and financial data. It is widely used by central banks and financial institutions to monitor long-term trends in the economy, and it can be used to identify turning points in the business cycle. The filter can also be used to analyze asset prices, exchange rates, and other financial variables.
The Hodrick-Prescott filter is a powerful tool for analyzing economic and financial data. It separates a time series into a trend component and a cyclical component, allowing for easy identification of long-term trends and turning points in the business cycle. While it has some limitations, it remains a valuable tool for economists, central banks, and financial institutions around the world.
STD/Clutter-Filtered, Variety FIR Filters [Loxx]STD/Clutter-Filtered, Variety FIR Filters is a FIR filter explorer. The following FIR Digital Filters are included.
Rectangular - simple moving average
Hanning
Hamming
Blackman
Blackman/Harris
Linear weighted
Triangular
There are 10s of windowing functions like the ones listed above. This indicator will be updated over time as I create more windowing functions in Pine.
Uniform/Rectangular Window
The uniform window (also called the rectangular window) is a time window with unity amplitude for all time samples and has the same effect as not applying a window.
Use this window when leakage is not a concern, such as observing an entire transient signal.
The uniform window has a rectangular shape and does not attenuate any portion of the time record. It weights all parts of the time record equally. Because the uniform window does not force the signal to appear periodic in the time record, it is generally used only with functions that are already periodic within a time record, such as transients and bursts.
The uniform window is sometimes called a transient or boxcar window.
For sine waves that are exactly periodic within a time record, using the uniform window allows you to measure the amplitude exactly (to within hardware specifications) from the Spectrum trace.
Hanning Window
The Hanning window attenuates the input signal at both ends of the time record to zero. This forces the signal to appear periodic. The Hanning window offers good frequency resolution at the expense of some amplitude accuracy.
This window is typically used for broadband signals such as random noise. This window should not be used for burst or chirp source types or other strictly periodic signals. The Hanning window is sometimes called the Hann window or random window.
Hamming Window
Computers can't do computations with an infinite number of data points, so all signals are "cut off" at either end. This causes the ripple on either side of the peak that you see. The hamming window reduces this ripple, giving you a more accurate idea of the original signal's frequency spectrum.
Blackman
The Blackman window is a taper formed by using the first three terms of a summation of cosines. It was designed to have close to the minimal leakage possible. It is close to optimal, only slightly worse than a Kaiser window.
Blackman-Harris
This is the original "Minimum 4-sample Blackman-Harris" window, as given in the classic window paper by Fredric Harris "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform", Proceedings of the IEEE, vol 66, no. 1, pp. 51-83, January 1978. The maximum side-lobe level is -92.00974072 dB.
Linear Weighted
A Weighted Moving Average puts more weight on recent data and less on past data. This is done by multiplying each bar’s price by a weighting factor. Because of its unique calculation, WMA will follow prices more closely than a corresponding Simple Moving Average.
Triangular Weighted
Triangular windowing is known for very smooth results. The weights in the triangular moving average are adding more weight to central values of the averaged data. Hence the coefficients are specifically distributed. Some of the examples that can give a clear picture of the coefficients progression:
period 1 : 1
period 2 : 1 1
period 3 : 1 2 1
period 4 : 1 2 2 1
period 5 : 1 2 3 2 1
period 6 : 1 2 3 3 2 1
period 7 : 1 2 3 4 3 2 1
period 8 : 1 2 3 4 4 3 2 1
Read here to read about how each of these filters compare with each other: Windowing
What is a Finite Impulse Response Filter?
In signal processing, a finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
Ultra Low Lag Moving Average's weights are designed to have MAXIMUM possible smoothing and MINIMUM possible lag compatible with as-flat-as-possible phase response.
What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Related Indicators
STD/Clutter-Filtered, Kaiser Window FIR Digital Filter
STD- and Clutter-Filtered, Non-Lag Moving Average
Clutter-Filtered, D-Lag Reducer, Spec. Ops FIR Filter
STD-Filtered, Ultra Low Lag Moving Average
Time-Based Fair Value Gaps (FVG) with Inversions (iFVG)Overview
The Time-Based Fair Value Gaps (FVG) with Inversions (iFVG) (ICT/SMT) indicator is a specialized tool designed for traders using Inner Circle Trader (ICT) methodologies. Inspired by LuxAlgo's Fair Value Gap indicator, this script introduces significant enhancements by integrating ICT principles, focusing on precise time-based FVG detection, inversion tracking, and retest signals tailored for institutional trading strategies. Unlike LuxAlgo’s general FVG approach, this indicator filters FVGs within customizable 10-minute windows aligned with ICT’s macro timeframes and incorporates ICT-specific concepts like mitigation, liquidity grabs, and session-based gap prioritization.
This tool is optimized for 1–5 minute charts, though probably best for 1 minute charts, identifying bullish and bearish FVGs, tracking their mitigation into inverted FVGs (iFVGs) as key support/resistance zones, and generating retest signals with customizable “Close” or “Wick” confirmation. Features like ATR-based filtering, optional FVG labels, mitigation removal, and session-specific FVG detection (e.g., first FVG in AM/PM sessions) make it a powerful tool for ICT traders.
Originality and Improvements
While inspired by LuxAlgo’s FVG indicator (credit to LuxAlgo for their foundational work), this script significantly extends the original concept by:
1. Time-Based FVG Detection: Unlike LuxAlgo’s continuous FVG identification, this script filters FVGs within user-defined 10-minute windows each hour (:00–:10, :10–:20, etc.), aligning with ICT’s emphasis on specific periods of institutional activity, such as hourly opens/closes or kill zones (e.g., New York 7:00–11:00 AM EST). This ensures FVGs are relevant to high-probability ICT setups.
2. Session-Specific First FVG Option: A unique feature allows traders to display only the first FVG in ICT-defined AM (9:30–10:00 AM EST) or PM (1:30–2:00 PM EST) sessions, reflecting ICT’s focus on initial market imbalances during key liquidity events.
3. ICT-Driven Mitigation and Inversion Logic: The script tracks FVG mitigation (when price closes through a gap) and converts mitigated FVGs into iFVGs, which serve as ICT-style support/resistance zones. This aligns with ICT’s view that mitigated gaps become critical reversal points, unlike LuxAlgo’s simpler gap display.
4. Customizable Retest Signals: Retest signals for iFVGs are configurable for “Close” (conservative, requiring candle body confirmation) or “Wick” (faster, using highs/lows), catering to ICT traders’ need for precise entry timing during liquidity grabs or Judas swings.
5. ATR Filtering and Mitigation Removal: An optional ATR filter ensures only significant FVGs are displayed, reducing noise, while mitigation removal declutters the chart by removing filled gaps, aligning with ICT’s principle that mitigated gaps lose relevance unless inverted.
6. Timezone and Timeframe Safeguards: A timezone offset setting aligns FVG detection with EST for ICT’s New York-centric strategies, and a timeframe warning alerts users to avoid ≥1-hour charts, ensuring accuracy in time-based filtering.
These enhancements make the script a distinct tool that builds on LuxAlgo’s foundation while offering ICT traders a tailored, high-precision solution.
How It Works
FVG Detection
FVGs are identified when a candle’s low is higher than the high of two candles prior (bullish FVG) or a candle’s high is lower than the low of two candles prior (bearish FVG). Detection is restricted to:
• User-selected 10-minute windows (e.g., :00–:10, :50–:60) to capture ICT-relevant periods like hourly transitions.
• AM/PM session first FVGs (if enabled), focusing on 9:30–10:00 AM or 1:30–2:00 PM EST for key market opens.
An optional ATR filter (default: 0.25× ATR) ensures only gaps larger than the threshold are displayed, prioritizing significant imbalances.
Mitigation and Inversion
When price closes through an FVG (e.g., below a bullish FVG’s bottom), the FVG is mitigated and becomes an iFVG, plotted as a support/resistance zone. iFVGs are critical in ICT for identifying reversal points where institutional orders accumulate.
Retest Signals
The script generates signals when price retests an iFVG:
• Close: Triggers when the candle body confirms the retest (conservative, lower noise).
• Wick: Triggers when the candle’s high/low touches the iFVG (faster, higher sensitivity). Signals are visualized with triangular markers (▲ for bullish, ▼ for bearish) and can trigger alerts.
Visualization
• FVGs: Displayed as colored boxes (green for bullish, red for bearish) with optional “Bull FVG”/“Bear FVG” labels.
• iFVGs: Shown as extended boxes with dashed midlines, limited to the user-defined number of recent zones (default: 5).
• Mitigation Removal: Mitigated FVGs/iFVGs are removed (if enabled) to keep the chart clean.
How to Use
Recommended Settings
• Timeframe: Use 1–5 minute charts for precision, avoiding ≥1-hour timeframes (a warning label appears if misconfigured).
• Time Windows: Enable :00–:10 and :50–:60 for hourly open/close FVGs, or use the “Show only 1st presented FVG” option for AM/PM session focus.
• ATR Filter: Keep enabled (multiplier 0.25–0.5) for significant gaps; disable on 1-minute charts for more FVGs during volatility.
• Signal Preference: Use “Close” for conservative entries, “Wick” for aggressive setups.
• Timezone Offset: Set to -5 for EST (or -4 for EDT) to align with ICT’s New York session.
Trading Strategy
1. Macro Timeframes: Focus on New York (7:00–11:00 AM EST) or London (2:00–5:00 AM EST) kill zones for high institutional activity.
2. FVG Entries: Trade bullish FVGs as support in uptrends or bearish FVGs as resistance in downtrends, especially in :00–:10 or :50–:60 windows.
3. iFVG Retests: Enter on retest signals (▲/▼) during liquidity grabs or Judas swings, using “Close” for confirmation or “Wick” for speed.
4. Session FVGs: Use the “Show only 1st presented FVG” option to target the first gap in AM/PM sessions, often tied to ICT’s market maker algorithms.
5. Risk Management: Combine with ICT concepts like order blocks or breaker blocks for confluence, and set stops beyond FVG/iFVG boundaries.
Alerts
Set alerts for:
• “Bullish FVG Detected”/“Bearish FVG Detected”: New FVGs in selected windows.
• “Bullish Signal”/“Bearish Signal”: iFVG retest confirmations.
Settings Description
• Show Last (1–100, default: 5): Number of recent iFVGs to display. Lower values reduce clutter.
• Show only 1st presented FVG : Limits FVGs to the first in 9:30–10:00 AM or 1:30–2:00 PM EST sessions (overrides time window checkboxes).
• Time Window Checkboxes: Enable/disable FVG detection in 10-minute windows (:00–:10, :10–:20, etc.). All enabled by default.
• Signal Preference: “Close” (default) or “Wick” for iFVG retest signals.
• Use ATR Filter: Enables ATR-based size filtering (default: true).
• ATR Multiplier (0–∞, default: 0.25): Sets FVG size threshold (higher values = larger gaps).
• Remove Mitigated FVGs: Removes filled FVGs/iFVGs (default: true).
• Show FVG Labels: Displays “Bull FVG”/“Bear FVG” labels (default: true).
• Timezone Offset (-12 to 12, default: -5): Aligns time windows with EST.
• Colors: Customize bullish (green), bearish (red), and midline (gray) colors.
Why Use This Indicator?
This indicator empowers ICT traders with a tool that goes beyond generic FVG detection, offering precise, time-filtered gaps and inversion tracking aligned with institutional trading principles. By focusing on ICT’s macro timeframes, session-specific imbalances, and customizable signal logic, it provides a clear edge for scalping, swing trading, or reversal setups in high-liquidity markets.
chrono_utilsLibrary "chrono_utils"
📝 Description
Collection of objects and common functions that are related to datetime windows session days and time ranges. The main purpose of this library is to handle time-related functionality and make it easy to reason about a future bar checking if it will be part of a predefined session and/or inside a datetime window. All existing session functionality I found in the documentation e.g. "not na(time(timeframe, session, timezone))" are not suitable for strategy scripts, since the execution of the orders is delayed by one bar, due to the script execution happening at the bar close. Moreover, a history operator with a negative value that looks forward is not allowed in any pinescript expression. So, a prediction for the next bar using the bars_back argument of "time()"" and "time_close()" was necessary. Thus, I created this library to overcome this small but very important limitation. In the meantime, I added useful functionality to handle session-based behavior. An interesting utility that emerged from this development is data anomaly detection where a comparison between the prediction and the actual value is happening. If those two values are different then a data inconsistency happens between the prediction bar and the actual bar (probably due to a holiday, half session day, a timezone change etc..)
🤔 How to Guide
To use the functionality this library provides in your script you have to import it first!
Copy the import statement of the latest release by pressing the copy button below and then paste it into your script. Give a short name to this library so you can refer to it later on. The import statement should look like this:
import jason5480/chrono_utils/2 as chr
To check if a future bar will be inside a window first of all you have to initialize a DateTimeWindow object.
A code example is the following:
var dateTimeWindow = chr.DateTimeWindow.new().init(fromDateTime = timestamp('01 Jan 2023 00:00'), toDateTime = timestamp('01 Jan 2024 00:00'))
Then you have to "ask" the dateTimeWindow if the future bar defined by an offset (default is 1 that corresponds th the next bar), will be inside that window:
// Filter bars outside of the datetime window
bool dateFilterApproval = dateTimeWindow.is_bar_included()
You can visualize the result by drawing the background of the bars that are outside the given window:
bgcolor(color = dateFilterApproval ? na : color.new(color.fuchsia, 90), offset = 1, title = 'Datetime Window Filter')
In the same way, you can "ask" the Session if the future bar defined by an offset it will be inside that session.
First of all, you should initialize a Session object.
A code example is the following:
var sess = chr.Session.new().from_sess_string(sess = '0800-1700:23456', refTimezone = 'UTC')
Then check if the given bar defined by the offset (default is 1 that corresponds th the next bar), will be inside the session like that:
// Filter bars outside the sessions
bool sessionFilterApproval = view.sess.is_bar_included()
You can visualize the result by drawing the background of the bars that are outside the given session:
bgcolor(color = sessionFilterApproval ? na : color.new(color.red, 90), offset = 1, title = 'Session Filter')
In case you want to visualize multiple session ranges you can create a SessionView object like that:
var view = SessionView.new().init(SessionDays.new().from_sess_string('2345'), array.from(SessionTimeRange.new().from_sess_string('0800-1600'), SessionTimeRange.new().from_sess_string('1300-2200')), array.from('London', 'New York'), array.from(color.blue, color.orange))
and then call the draw method of the SessionView object like that:
view.draw()
🏋️♂️ Please refer to the "EXAMPLE DATETIME WINDOW FILTER" and "EXAMPLE SESSION FILTER" regions of the script for more advanced code examples of how to utilize the full potential of this library, including user input settings and advanced visualization!
⚠️ Caveats
As I mentioned in the description there are some cases that the prediction of the next bar is not accurate. A wrong prediction will affect the outcome of the filtering. The main reasons this could happen are the following:
Public holidays when the market is closed
Half trading days usually before public holidays
Change in the daylight saving time (DST)
A data anomaly of the chart, where there are missing and/or inconsistent data.
A bug in this library (Please report by PM sending the symbol, timeframe, and settings)
Special thanks to @robbatt and @skinra for the constructive feedback 🏆. Without them, the exposed API of this library would be very lengthy and complicated to use. Thanks to them, now the user of this library will be able to get the most, with only a few lines of code!
Relational Quadratic Kernel Channel [Vin]The Relational Quadratic Kernel Channel (RQK-Channel-V) is designed to provide more valuable potential price extremes or continuation points in the price trend.
Example:
Usage:
Lookback Window: Adjust the "Lookback Window" parameter to control the number of previous bars considered when calculating the Rational Quadratic Estimate. Longer windows capture longer-term trends, while shorter windows respond more quickly to price changes.
Relative Weight: The "Relative Weight" parameter allows you to control the importance of each data point in the calculation. Higher values emphasize recent data, while lower values give more weight to historical data.
Source: Choose the data source (e.g., close price) that you want to use for the kernel estimate.
ATR Length: Set the length of the Average True Range (ATR) used for channel width calculation. A longer ATR length results in wider channels, while a shorter length leads to narrower channels.
Channel Multipliers: Adjust the "Channel Multiplier" parameters to control the width of the channels. Higher multipliers result in wider channels, while lower multipliers produce narrower channels. The indicator provides three sets of channels, each with its own multiplier for flexibility.
Details:
Rational Quadratic Kernel Function:
The Rational Quadratic Kernel Function is a type of smoothing function used to estimate a continuous curve or line from discrete data points. It is often used in time series analysis to reduce noise and emphasize trends or patterns in the data.
The formula for the Rational Quadratic Kernel Function is generally defined as:
K(x) = (1 + (x^2) / (2 * α * β))^(-α)
Where:
x represents the distance or difference between data points.
α and β are parameters that control the shape of the kernel. These parameters can be adjusted to control the smoothness or flexibility of the kernel function.
In the context of this indicator, the Rational Quadratic Kernel Function is applied to a specified source (e.g., close prices) over a defined lookback window. It calculates a smoothed estimate of the source data, which is then used to determine the central value of the channels. The kernel function allows the indicator to adapt to different market conditions and reduce noise in the data.
The specific parameters (length and relativeWeight) in your indicator allows to fine-tune how the Rational Quadratic Kernel Function is applied, providing flexibility in capturing both short-term and long-term trends in the data.
To know more about unsupervised ML implementations, I highly recommend to follow the users, @jdehorty and @LuxAlgo
Optimizing the parameters:
Lookback Window (length): The lookback window determines how many previous bars are considered when calculating the kernel estimate.
For shorter-term trading strategies, you may want to use a shorter lookback window (e.g., 5-10).
For longer-term trading or investing, consider a longer lookback window (e.g., 20-50).
Relative Weight (relativeWeight): This parameter controls the importance of each data point in the calculation.
A higher relative weight (e.g., 2 or 3) emphasizes recent data, which can be suitable for trend-following strategies.
A lower relative weight (e.g., 1) gives more equal importance to historical and recent data, which may be useful for strategies that aim to capture both short-term and long-term trends.
ATR Length (atrLength): The length of the Average True Range (ATR) affects the width of the channels.
Longer ATR lengths result in wider channels, which may be suitable for capturing broader price movements.
Shorter ATR lengths result in narrower channels, which can be helpful for identifying smaller price swings.
Channel Multipliers (channelMultiplier1, channelMultiplier2, channelMultiplier3): These parameters determine the width of the channels relative to the ATR.
Adjust these multipliers based on your risk tolerance and desired channel width.
Higher multipliers result in wider channels, which may lead to fewer signals but potentially larger price movements.
Lower multipliers create narrower channels, which can result in more frequent signals but potentially smaller price movements.
STD/C-Filtered, N-Order Power-of-Cosine FIR Filter [Loxx]STD/C-Filtered, N-Order Power-of-Cosine FIR Filter is a Discrete-Time, FIR Digital Filter that uses Power-of-Cosine Family of FIR filters. This is an N-order algorithm that turns the following indicator from a static max 16 orders to a N orders, but limited to 50 in code. You can change the top end value if you with to higher orders than 50, but the signal is likely too noisy at that level. This indicator also includes a clutter and standard deviation filter.
See the static order version of this indicator here:
STD/C-Filtered, Power-of-Cosine FIR Filter
Amplitudes for STD/C-Filtered, N-Order Power-of-Cosine FIR Filter:
What are FIR Filters?
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages.
What is Power-of-Sine Digital FIR Filter?
Also called Cos^alpha Window Family. In this family of windows, changing the value of the parameter alpha generates different windows.
f(n) = math.cos(alpha) * (math.pi * n / N) , 0 ≤ |n| ≤ N/2
where alpha takes on integer values and N is a even number
General expanded form:
alpha0 - alpha1 * math.cos(2 * math.pi * n / N)
+ alpha2 * math.cos(4 * math.pi * n / N)
- alpha3 * math.cos(4 * math.pi * n / N)
+ alpha4 * math.cos(6 * math.pi * n / N)
- ...
Special Cases for alpha:
alpha = 0: Rectangular window, this is also just the SMA (not included here)
alpha = 1: MLT sine window (not included here)
alpha = 2: Hann window (raised cosine = cos^2)
alpha = 4: Alternative Blackman (maximized roll-off rate)
This indicator contains a binomial expansion algorithm to handle N orders of a cosine power series. You can read about how this is done here: The Binomial Theorem
What is Pascal's Triangle and how was it used here?
In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia, China, Germany, and Italy.
The rows of Pascal's triangle are conventionally enumerated starting with row n = 0 at the top (the 0th row). The entries in each row are numbered from the left beginning with k=0 and are usually staggered relative to the numbers in the adjacent rows. The triangle may be constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is constructed by adding the number above and to the left with the number above and to the right, treating blank entries as 0. For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1), whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row.
Rows of Pascal's Triangle
0 Order: 1
1 Order: 1 1
2 Order: 1 2 1
3 Order: 1 3 3 1
4 Order: 1 4 6 4 1
5 Order: 1 5 10 10 5 1
6 Order: 1 6 15 20 15 6 1
7 Order: 1 7 21 35 35 21 7 1
8 Order: 1 8 28 56 70 56 28 8 1
9 Order: 1 9 36 34 84 126 126 84 36 9 1
10 Order: 1 10 45 120 210 252 210 120 45 10 1
11 Order: 1 11 55 165 330 462 462 330 165 55 11 1
12 Order: 1 12 66 220 495 792 924 792 495 220 66 12 1
13 Order: 1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
For a 12th order Power-of-Cosine FIR Filter
1. We take the coefficients from the Left side of the 12th row
1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1
2. We slice those in half to
1 13 78 286 715 1287 1716
3. We reverse the array
1716 1287 715 286 78 13 1
This is our array of alphas: alpha1, alpha2, ... alphaN
4. We then pull alpha one from the previous order, order 11, the middle value
11 Order: 1 11 55 165 330 462 462 330 165 55 11 1
The middle value is 462, this value becomes our alpha0 in the calculation
5. We apply these alphas to the cosine calculations
example: + alpha4 * math.cos(6 * math.pi * n / N)
6. We then divide by the sum of the alphas to derive our final coefficient weighting kernel
**This is only useful for orders that are EVEN, if you use odd ordering, the following are the coefficient outputs and these aren't useful since they cancel each other out and result in a value of zero. See below for an odd numbered oder and compare with the amplitude of the graphic posted above of the even order amplitude:
What is a Standard Deviation Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.
What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
STD/C-Filtered, Power-of-Cosine FIR Filter [Loxx]STD/C-Filtered, Power-of-Cosine FIR Filter is a Discrete-Time, FIR Digital Filter that uses Power-of-Cosine Family of FIR filters. This indicator also includes a clutter and standard deviation filter.
Amplitudes
What are FIR Filters?
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages.
What is Power-of-Sine Digital FIR Filter?
Also called Cos^alpha Window Family. In this family of windows, changing the value of the parameter alpha generates different windows.
f(n) = math.cos(alpha) * (math.pi * n / N) , 0 ≤ |n| ≤ N/2
where alpha takes on integer values and N is a even number
General expanded form:
alpha0 - alpha1 * math.cos(2 * math.pi * n / N)
+ alpha2 * math.cos(4 * math.pi * n / N)
- alpha3 * math.cos(4 * math.pi * n / N)
+ alpha4 * math.cos(6 * math.pi * n / N)
- ...
Special Cases for alpha:
alpha = 0: Rectangular window, this is also just the SMA (not included here)
alpha = 1: MLT sine window (not included here)
alpha = 2: Hann window (raised cosine = cos^2)
alpha = 4: Alternative Blackman (maximized roll-off rate)
For this indicator, I've included alpha values from 2 to 16
What is a Standard Devaition Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.
What is a Clutter Filter?
For our purposes here, this is a filter that compares the slope of the trading filter output to a threshold to determine whether to shift trends. If the slope is up but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. If the slope is down but the slope doesn't exceed the threshold, then the color is gray and this indicates a chop zone. Alternatively if either up or down slope exceeds the threshold then the trend turns green for up and red for down. Fro demonstration purposes, an EMA is used as the moving average. This acts to reduce the noise in the signal.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Price Imbalance as Consecutive Levels of AveragesOverview
The Price Imbalance as Consecutive Levels of Averages indicator is an advanced technical analysis tool designed to identify and visualize price imbalances in financial markets. Unlike traditional moving average (MA) indicators that update continuously with each new price bar, this indicator employs moving averages calculated over consecutive, non-overlapping historical windows. This unique approach leverages comparative historical data to provide deeper insights into trend strength and potential reversals, offering traders a more nuanced understanding of market dynamics and reducing the likelihood of false signals or fakeouts.
Key Features
Consecutive Rolling Moving Averages: Utilizes three distinct simple moving averages (SMAs) calculated over consecutive, non-overlapping windows to capture different historical segments of price data.
Dynamic Color-Coded Visualization: SMA lines change color and style based on the relationship between the averages, highlighting both extreme and normal market conditions.
Median and Secondary Median Lines: Provides additional layers of price distribution insight during normal trend conditions through the plotting of primary and secondary median lines.
Fakeout Prevention: Filters out short-term volatility and sharp price movements by requiring consistent historical alignment of multiple moving averages.
Customizable Parameters: Offers flexibility to adjust SMA window lengths and line extensions to align with various trading strategies and timeframes.
Real-Time Updates with Historical Context: Continuously recalculates and updates SMA lines based on comparative historical windows, ensuring that the indicator reflects both current and past market conditions.
Inputs & Settings
Rolling Window Lengths:
Window 1 Length (Most Recent) Bars: Number of bars used to calculate the most recent SMA. (Default: 5, Range: 2–300)
Window 2 Length (Preceding) Bars: Number of bars for the second SMA, shifted by Window 1. (Default: 8, Range: 2–300)
Window 3 Length (Third Rolling) Bars: Number of bars for the third SMA, shifted by the combined lengths of Window 1 and Window 2. (Default: 13, Range: 2–300)
Horizontal Line Extension:
Horizontal Line Extension (Bars): Determines how far each SMA line extends horizontally on the chart. (Default: 10 bars, Range: 1–100)
Functionality and Theory
1. Calculating Consecutive Simple Moving Averages (SMAs):
The indicator calculates three SMAs, each based on distinct and consecutive historical windows of price data. This approach contrasts with traditional MAs that continuously update with each new price bar, offering a static view of past trends rather than an ongoing one.
Mean1 (SMA1): Calculated over the most recent Window 1 Length bars. Represents the short-term trend.
Mean1=∑i=1N1CloseiN1
Mean1=N1∑i=1N1Closei
Where N1N1 is the length of Window 1.
Mean2 (SMA2): Calculated over the preceding Window 2 Length bars, shifted back by Window 1 Length bars. Represents the medium-term trend.
\text{Mean2} = \frac{\sum_{i=1}^{N_2} \text{Close}_{i + N_1}}}{N_2}
Where N2N2 is the length of Window 2.
Mean3 (SMA3): Calculated over the third rolling Window 3 Length bars, shifted back by the combined lengths of Window 1 and Window 2 bars. Represents the long-term trend.
\text{Mean3} = \frac{\sum_{i=1}^{N_3} \text{Close}_{i + N_1 + N_2}}}{N_3}
Where N3N3 is the length of Window 3.
2. Determining Market Conditions:
The relationship between the three SMAs categorizes the market condition into either extreme or normal states, enabling traders to quickly assess trend strength and potential reversals.
Extreme Bullish:
Mean3Mean2>Mean1
Mean3>Mean2>Mean1
Indicates a strong and sustained downward trend. SMA lines are colored purple and styled as dashed lines.
Normal Bullish:
Mean1>Mean2andnot in extreme bullish condition
Mean1>Mean2andnot in extreme bullish condition
Indicates a standard upward trend. SMA lines are colored green and styled as solid lines.
Normal Bearish:
Mean1Mean2>Mean1
Mean3>Mean2>Mean1
Normal Bullish:
Mean1>Mean2andnot in Extreme Bullish
Mean1>Mean2andnot in Extreme Bullish
Normal Bearish:
Mean1 Mean2 > Mean3
Visualization: All three SMAs are displayed as gold dashed lines.
Median Lines: Not displayed to maintain chart clarity.
Interpretation: Indicates a strong and sustained upward trend. Traders may consider entering long positions, confident in the trend's strength without the distraction of additional lines.
2. Normal Bullish Condition:
SMAs Alignment: Mean1 > Mean2 (not in extreme condition)
Visualization: Mean1 and Mean2 are green solid lines; Mean3 is gray.
Median Lines: A thin blue dotted median line is plotted between Mean1 and Mean2, with two additional thin blue dashed lines as secondary medians.
Interpretation: Confirms an upward trend while providing deeper insights into price distribution. Traders can use the median and secondary median lines to identify optimal entry points and manage risk more effectively.
3. Extreme Bearish Condition:
SMAs Alignment: Mean3 > Mean2 > Mean1
Visualization: All three SMAs are displayed as purple dashed lines.
Median Lines: Not displayed to maintain chart clarity.
Interpretation: Indicates a strong and sustained downward trend. Traders may consider entering short positions, confident in the trend's strength without the distraction of additional lines.
4. Normal Bearish Condition:
SMAs Alignment: Mean1 < Mean2 (not in extreme condition)
Visualization: Mean1 and Mean2 are red solid lines; Mean3 is gray.
Median Lines: A thin blue dotted median line is plotted between Mean1 and Mean2, with two additional thin blue dashed lines as secondary medians.
Interpretation: Confirms a downward trend while providing deeper insights into price distribution. Traders can use the median and secondary median lines to identify optimal entry points and manage risk more effectively.
Customization and Flexibility
The Price Imbalance as Consecutive Levels of Averages indicator is highly adaptable, allowing traders to tailor it to their specific trading styles and market conditions through adjustable parameters:
SMA Window Lengths: Modify the lengths of Window 1, Window 2, and Window 3 to capture different historical trend segments, whether focusing on short-term fluctuations or long-term movements.
Line Extension: Adjust the horizontal extension of SMA and median lines to align with different trading horizons and chart preferences.
Color and Style Preferences: While default colors and styles are optimized for clarity, traders can customize these elements to match their personal chart aesthetics and enhance visual differentiation.
This flexibility ensures that the indicator remains versatile and applicable across various markets, asset classes, and trading strategies, providing valuable insights tailored to individual trading needs.
Conclusion
The Price Imbalance as Consecutive Levels of Averages indicator offers a comprehensive and innovative approach to analyzing price trends and imbalances within financial markets. By utilizing three consecutive, non-overlapping SMAs and incorporating median lines during normal trend conditions, the indicator provides clear and actionable insights into trend strength and price distribution. Its unique design leverages comparative historical data, distinguishing it from traditional moving averages and enhancing its utility in identifying genuine market movements while minimizing false signals. This dynamic and customizable tool empowers traders to refine their technical analysis, optimize their trading strategies, and navigate the markets with greater confidence and precision.
Physics CandlesPhysics Candles embed volume and motion physics directly onto price candles or market internals according to the cyclic pattern of financial securities. The indicator works on both real-time “ticks” and historical data using statistical modeling to highlight when these values, like volume or momentum, is unusual or relatively high for some periodic window in time. Each candle is made out of one or more sub-candles that each contain their own information of motion, which converts to the color and transparency, or brightness, of that particular candle segment. The segments extend throughout the entire candle, both body and wicks, and Thick Wicks can be implemented to see the color coding better. This candle segmentation allows you to see if all the volume or energy is evenly distributed throughout the candle or highly contained in one small portion of it, and how intense these values are compared to similar time periods without going to lower time frames. Candle segmentation can also change a trader’s perspective on how valuable the information is. A “low” volume candle, for instance, could signify high value short-term stopping volume if the volume is all concentrated in one segment.
The Candles are flexible. The physics information embedded on the candles need not be from the same price security or market internal as the chart when using the Physics Source option, and multiple Candles can be overlayed together. You could embed stock price Candles with market volume, market price Candles with stock momentum, market structure with internal acceleration, stock price with stock force, etc. My particular use case is scalping the SPX futures market (ES), whose price action is also dictated by the volume action in the associated cash market, or SPY, as well as a host of other securities. Physics allows you to embed the ES volume on the SPY price action, or the SPY volume on the ES price action, or you can combine them both by overlaying two Candle streams and increasing the Number of Overlays option to two. That option decreases the transparency levels of your coloring scheme so that overlaying multiple Candles converges toward the same visual color intensity as if you had one. The Candle and Physics Sources allows for both Symbols and Spreads to visualize Candle physics from a single ticker or some mathematical transformation of tickers.
Due to certain TradingView programming restrictions, each Candle can only be made out of a maximum of 8 candle segments, or an “8-bit” resolution. Since limits are just an opportunity to go beyond, the user has the option to stack multiple Candle indicators together to further increase the candle resolution. If you don’t want to see the Candles for some particular period of the day, you can hide them, or use the hiding feature to have multiple Candles calibrated to show multiple parts of the trading day. Securities tend to have low volume after hours with sharp spikes at the open or close. Multiple Candles can be used for multiple parts of the trading day to accommodate these different cycles in volume.
The Candles do not need be associated with the nominal security listed on the TV chart. The Candle Source allows the user to look at AAPL Candles, for instance, while on a TSLA or SPY chart, each with their respective volume actions integrated into the candles, for instance, to allow the user to see multiple security price and volume correlation on a single chart.
The physics information currently embeddable on Candles are volume or time, velocity, momentum, acceleration, force, and kinetic energy. In order to apply equations of motion containing a mass variable to financial securities, some analogous value for mass must be assumed. Traders often regard volume or time as inextricable variables to a securities price that can indicate the direction and strength of a move. Since mass is the inextricable variable to calculating the momentum, force, or kinetic energy of motion, the user has the option to assume either time or volume is analogous to mass. Volume may be a better option for mass as it is not strictly dependent on the speed of a security, whereas time is.
Data transformations and outlier statistics are used to color code the intensity of the physics for each candle segment relative to past periodic behavior. A million shares during pre-market or a million shares during noontime may be more intense signals than a typical million shares traded at the open, and should have more intense color signals. To account for a specific cyclic behavior in the market, the user can specify the Window and Cycle Time Frames. The Window Time Frame splits up a Cycle into windows, samples and aggregates the statistics for each window, then compares the current physics values against past values in the same window. Intraday traders may benefit from using a Daily Cycle with a 30-minute Window Time Frame and 1-minute Sample Time Frame. These settings sample and compare the physics of 1-minute candles within the current 30-minute window to the same 30-minute window statistics for all past trading days, up until the data limit imposed by TradingView, or until the Data Collection Start Date specified in the settings. Longer-term traders may benefit from using a Monthly Cycle with a Weekly Time Frame, or a Yearly Cycle with a Quarterly Time Frame.
Multiple statistics and data transformation methods are available to convey relative intensity in different ways for different trading signals. Physics Candles allows for both Normal and Log-Normal assumptions in the physics distribution. The data can then be transformed by Linear, Logarithmic, Z-Score, or Power-Law scoring, where scoring simply assigns an intensity to the relative physics value of each candle segment based on some mathematical transformation. Z-scoring often renders adequate detection by scoring the segment value, such as volume or momentum, according to the mean and standard deviation of the data set in each window of the cycle. Logarithmic or power-law transformation with a gamma below 1 decreases the disparity between intensities so more less-important signals will show up, whereas the power-law transformation with gamma values above 1 increases the disparity between intensities, so less more-important signals will show up. These scores are then converted to color and transparency between the Min Score and the Max Score Cutoffs. The Auto-Normalization feature can automatically pick these cutoffs specific to each window based on the mean and standard deviation of the data set, or the user can manually set them. Physics was developed with novices in mind so that most users could calibrate their own settings by plotting the candle segment distributions directly on the chart and fiddling with the settings to see how different cutoffs capture different portions of the distribution and affect the relative color intensities differently. Security distributions are often skewed with fat-tails, known as kurtosis, where high-volume segments for example, have a higher-probabilities than expected for a normal distribution. These distribution are really log-normal, so that taking the logarithm leads to a standard bell-shaped distribution. Taking the Z-score of the Log-Normal distribution could make the most statistical sense, but color sensitivity is a discretionary preference.
Background Philosophy
This indicator was developed to study and trade the physics of motion in financial securities from a visually intuitive perspective. Newton’s laws of motion are loosely applied to financial motion:
“A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force”.
Financial securities remain at rest, or in motion at constant speed up or down, unless acted upon by the force of traders exchanging securities.
“When a body is acted upon by a force, the time rate of change of its momentum equals the force”.
Momentum is the product of mass and velocity, and force is the product of mass and acceleration. Traders render force on the security through the mass of their trading activity and the acceleration of price movement.
“If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.”
Force arises from the interaction of traders, buyers and sellers. One body of motion, traders’ capitalization, exerts an equal and opposite force on another body of motion, the financial security. A securities movement arises at the expense of a buyer or seller’s capitalization.
Volume
The premise of this indicator assumes that volume, v, is an analogous means of measuring physical mass, m. This premise allows the application of the equations of motion to the movement of financial securities. We know from E=mc^2 that mass has energy. Energy can be used to create motion as kinetic energy. Taking a simple hypothetical example, the interaction of one short seller looking to cover lower and one buyer looking to sell higher exchange shares in a security at an agreed upon price to create volume or mass, and therefore, potential energy. Eventually the short seller will actively cover and buy the security from the previous buyer, moving the security higher, or the buyer will actively sell to the short seller, moving the security lower. The potential energy inherent in the initial consolidation or trading activity between buy and seller is now converted to kinetic energy on the subsequent trading activity that moves the securities price. The more potential energy that is created in the consolidation, the more kinetic energy there is to move price. This is why point and figure traders are said to give price targets based on the level of volatility or size of a consolidation range, or why Gann traders square price and time, as time is roughly proportional to mass and trading activity. The build-up of potential energy between short sellers and buyers in GME or TSLA led to their explosive moves beyond their standard fundamental valuations.
Position
Position, p, is simply the price or value of a financial security or market internal.
Time
Time, t, is another means of measuring mass to discover price behavior beyond the time snapshots that simple candle charts provide. We know from E=mc^2 that time is related to rest mass and energy given the speed of light, c, where time ≈ distance * sqrt(mass/E). This relation can also be derived from F=ma. The more mass there is, the longer it takes to compute the physics of a system. The more energy there is, the shorter it takes to compute the physics of a system. Similarly, more time is required to build a “resting” low-volatility trading consolidation with more mass. More energy added to that trading consolidation by competing buyers and sellers decreases the time it takes to build that same mass. Time is also related to price through velocity.
Velocity = (p(t1) – p(t0)) / p(t0)
Velocity, v, is the relative percent change of a securities price, p, over a period of time, t0 to t1. The period of time is between subsequent candles, and since time is constant between candles within the same timeframe, it is not used to calculate velocity or acceleration. Price moves faster with higher velocity, and slower with slower velocity, over the same fixed period of time. The product of velocity and mass gives momentum.
Momentum = mv
This indicator uses physics definition of momentum, not finance’s. In finance, momentum is defined as the amount of change in a securities price, either relative or absolute. This is definition is unfortunate, pun intended, since a one dollar move in a security from a thousand shares traded between a few traders has the exact same “momentum” as a one dollar move from millions of shares traded between hundreds of traders with everything else equal. If momentum is related to the energy of the move, momentum should consider both the level of activity in a price move, and the amount of that price move. If we equate mass to volume to account for the level of trading activity and use physics definition of momentum as the product of mass and velocity, this revised definition now gives a thousand-times more momentum to a one-dollar price move that has a thousand-times more volume behind it. If you want to use finance’s volume-less definition of momentum, use velocity in this indicator.
Acceleration = v(t1) – v(t0)
Acceleration, a, is the difference between velocities over some period of time, t0 to t1. Positive acceleration is necessary to increase a securities speed in the positive direction, while negative acceleration is necessary to decrease it. Acceleration is related to force by mass.
Force = ma
Force is required to change the speed of a securities valuation. Price movements with considerable force have considerably more impact on future direction. A change in direction requires force.
Kinetic Energy = 0.5mv^2
Kinetic energy is the energy that a financial security gains from the change in its velocity by force. The built-up of potential energy in trading consolidations can be converted to kinetic energy on a breakout from the consolidation.
Cycle Theory and Relativity
Just as the physics of motion is relative to a point of reference, so too should the physics of financial securities be relative to a point of reference. An object moving at a 100 mph towards another object moving in the same direction at 100 mph will not appear to be moving relative to each other, nor will they collide, but from an outsider observer, the objects are going 100 mph and will collide with significant impact if they run into a stationary object relative to the observer. Similarly, trading with a hundred thousand shares at the open when the average volume is a couple million may have a much smaller impact on the price compared to trading a hundred thousand shares pre-market when the average volume is ten thousand shares. The point of reference used in this indicator is the average statistics collected for a given Window Time Frame for every Cycle Time Frame. The physics values are normalized relative to these statistics.
Examples
The main chart of this publication shows the Force Candles for the SPY. An intense force candle is observed pre-market that implicates the directional overtone of the day. The assumption that direction should follow force arises from physical observation. If a large object is accelerating intensely in a particular direction, it may be fair to assume that the object continues its direction for the time being unless acted upon by another force.
The second example shows a similar Force Candle for the SPY that counters the assumption made in the first example and emphasizes the importance of both motion and context. While it’s fair to assume that a heavy highly accelerating object should continue its course, if that object runs into an obstacle, say a brick wall, it’s course may deviate. This example shows SPY running into the 50% retracement wall from the low of Mar 2020, a significant support level noted in literature. The example also conveys Gann’s idea of “lost motion”, where the SPY penetrated the 50% price but did not break through it. A brick wall is not one atom thick and price support is not one tick thick. An object can penetrate only one layer of a wall and not go through it.
The third example shows how Volume Candles can be used to identify scalping opportunities on the SPY and conveys why price behavior is as important as motion and context. It doesn’t take a brick wall to impede direction if you know that the person driving the car tends to forget to feed the cats before they leave. In the chart below, the SPY breaks down to a confluence of the 5-day SMA, 20-day SMA, and an important daily trendline (not shown) after the bullish bounce from the 50% retracement days earlier. High volume candles on the SMA signify stopping volume that reverse price direction. The character of the day changes. Bulls become more aggressive than bears with higher volume on upswings and resistance, whiles bears take on a defensive position with lower volume on downswings and support. High volume stopping candles are seen after rallies, and can tell you when to take profit, get out of a position, or go short. The character change can indicate that its relatively safe to re-enter bullish positions on many major supports, especially given the overarching bullish theme from the large reaction off the 50% retracement level.
The last example emphasizes the importance of relativity. The Volume Candles in the chart below are brightest pre-market even though the open has much higher volume since the pre-market activity is much higher compared to past pre-markets than the open is compared to past opens. Pre-market behavior is a good indicator for the character of the day. These bullish Volume Candles are some of the brightest seen since the bounce off the 50% retracement and indicates that bulls are making a relatively greater attempt to bring the SPY higher at the start of the day.
Infrequently Asked Questions
Where do I start?
The default settings are what I use to scalp the SPY throughout most of the extended trading day, on a one-minute chart using SPY volume. I also overlay another Candle set containing ES future volume on the SPY price structure by setting the Physics Source to ES1! and the Number of Overlays setting to 2 for each Candle stream in order to account for pre- and post-market trading activity better. Since the closing volume is exponential-like up until the end of the regular trading day, adding additional Candle streams with a tighter Window Time Frame (e.g., 2-5 minute) in the last 15 minutes of trading can be beneficial. The Hide feature can allow you to set certain intraday timeframes to hide one Candle set in order to show another Candle set during that time.
How crazy can you get with this indicator?
I hope you can answer this question better. One interesting use case is embedding the velocity of market volume onto an internal market structure. The PCTABOVEVWAP.US is a market statistic that indicates the percent of securities above their VWAP among US stocks and is helpful for determining short term trends in the US market. When securities are rising above their VWAP, the average long is up on the day and a rising PCTABOVEVWAP.US can be viewed as more bullish. When securities are falling below their VWAP, the average short is up on the day and a falling PCTABOVEVWAP.US can be viewed as more bearish. (UPVOL.US - DNVOL.US) / TVOL.US is a “spread” symbol, in TV parlance, that indicates the decimal percent difference between advancing volume and declining volume in the US market, showing the relative flow of volume between stocks that are up on the day, and stocks that are down on the day. Setting PCTABOVEVWAP.US in the Candle Source, (UPVOL.US - DNVOL.US) / TVOL.US in the Physics Source, and selecting the Physics to Velocity will embed the relative velocity of the spread symbol onto the PCTABOVEVWAP.US candles. This can be helpful in seeing short term trends in the US market that have an increasing amount of volume behind them compared to other trends. The chart below shows Volume Candles (top) and these Spread Candles (bottom). The first top at 9:30 and second top at 10:30, the high of the day, break down when the spread candles light up, showing a high velocity volume transfer from up stocks to down stocks.
How do I plot the indicator distribution and why should I even care?
The distribution is visually helpful in seeing how different normalization settings effect the distribution of candle segments. It is also helpful in seeing what physics intensities you want to ignore or show by segmenting part of the distribution within the Min and Max Cutoff values. The intensity of color is proportional to the physics value between the Min and Max Cutoff values, which correspond to the Min and Max Colors in your color scheme. Any physics value outside these Min and Max Cutoffs will be the same as the Min and Max Colors.
Select the Print Windows feature to show the window numbers according to the Cycle Time Frame and Window Time Frame settings. The window numbers are labeled at the start of each window and are candle width in size, so you may need to zoom into to see them. Selecting the Plot Window feature and input the window number of interest to shows the distribution of physics values for that particular window along with some statistics.
A log-normal volume distribution of segmented z-scores is shown below for 30-minute opening of the SPY. The Min and Max Cutoff at the top of the graph contain the part of the distribution whose intensities will be linearly color-coded between the Min and Max Colors of the color scheme. The part of the distribution below the Min Cutoff will be treated as lowest quality signals and set to the Min Color, while the few segments above the Max Cutoff will be treated as the highest quality signals and set to the Max Color.
What do I do if I don’t see anything?
Troubleshooting issues with this indicator can involve checking for error messages shown near the indicator name on the chart or using the Data Validation section to evaluate the statistics and normalization cutoffs. For example, if the Plot Window number is set to a window number that doesn’t exist, an error message will tell you and you won’t see any candles. You can use the Print Windows option to show windows that do exist for you current settings. The auto-normalization cutoff values may be inappropriate for your particular use case and literally cut the candles out of the chart. Try changing the chart time frame to see if they are appropriate for your cycle, sample and window time frames. If you get a “Timeframe passed to the request.security_lower_tf() function must be lower than the timeframe of the main chart” error, this means that the chart timeframe should be increased above the sample time frame. If you get a “Symbol resolve error”, ensure that you have correct symbol or spread in the Candle or Physics Source.
How do I see a relative physics values without cycles?
Set the Window Time Frame to be equal to the Cycle Time Frame. This will aggregate all the statistics into one bucket and show the physics values, such as volume, relative to all the past volumes that TV will allow.
How do I see candles without segmentation?
Segmentation can be very helpful in one context or annoying in another. Segmentation can be removed by setting the candle resolution value to 1.
Notes
I have yet to find a trading platform that consistently provides accurate real-time volume and pricing information, lacking adequate end-user data validation or quality control. I can provide plenty of examples of real-time volume counts or prices provided by TradingView and other platforms that were significantly off from what they should have been when comparing against the exchanges own data, and later retroactively corrected or not corrected at all. Since no indicator can work accurately with inaccurate data, please use at your own discretion.
The first version is a beta version. Debugging and validating code in Pine script is difficult without proper unit testing. Please report any bugs with enough information to reproduce them and indicate why they are important. I also encourage you to export the data from TradingView and verify the calculations for your particular use case.
The indicator works on real-time updates that occur at a higher frequency than the candle time frame, which TV incorrectly refers to as ticks. They use this terminology inaccurately as updates are really aggregated tick data that can take place at different prices and may not accurately reflect the real tick price action. Consequently, this inaccuracy also impacts the real-time segmentation accuracy to some degree. TV does not provide a means of retaining “tick” information, so the higher granularity of information seen real-time will be lost on a disconnect.
TV does not provide time and sales information. The volume and price information collected using the Sample Time Frame is intraday, which provides only part of the picture. Intraday volume is generally 50 to 80% of the end of day volume. Consequently, the daily+ OHLC prices are intraday, and may differ significantly from exchanged settled OHLC prices.
The Cycle and Window Time Frames refer to calendar days and time, not trading days or time. For example, the first window week of a monthly cycle is the first seven days of the month, not the first Monday through Friday of trading for the month.
Chart Time Frames that are higher than the Window Time Frames average the normalized physics for price action that occurred within a given Candle segment. It does not average price action that did not occur.
One of the main performance bottleneck in TradingView’s Pine Script is client-side drawing and plotting. The performance of this indicator can be increased by lowering the resolution (the number of sub-candles this indicator plots), getting a faster computer, or increasing the performance of your computer like plugging your laptop in and eliminating unnecessary processes.
The statistical integrity of this indicator relies on the number of samples collected per sample window in a given cycle. Higher sample counts can be obtained by increasing the chart time frame or upgrading the TradingView plan for a higher bar count. While increasing the chart time frame doesn’t increase the visual number of bars plotted on the chart, it does increase the number of bars that can be pulled at a lower time frame, up to 100,000.
Due to a limitation in Pine Scripts request_lower_tf() function, using a spread symbol will only work for regular trading hours, not extended trading hours.
Ideally, velocity or momentum should be calculated between candle closes. To eliminate the need to deal with price gaps that would lead to an incorrect statistical distributions, momentum is calculated between candle open and closes as a percent change of the price or value, which should not be an issue for most liquid securities.
Stock WatchOverview
Watch list are very common in trading, but most of them simply provide the means of tracking a list of symbols and their current price. Then, you click through the list and perform some additional analysis individually from a chart setup. What this indicator is designed to do is provide a watch list that employs a high/low price range analysis in a table view across multiple time ranges for a much faster analysis of the symbols you are watching.
Discussion
The concept of this Stock Watch indicator is best understood when you think in terms of a 52 Week Range indication on many financial web sites. Taken a given symbol, what is the high and the low over a 52 week range and then determine where current price is within that range from a percentage perspective between 0% and 100%.
With this concept in mind, let's see how this Stock Watch indicator is meant to benefit.
There are four different H/L ranges relative to the chart's setting and a Scope property. Let's use a three month (3M) chart as our example and set the indicator's Scope = 4. A 3M chart provides three months of data in a single candle, now when we set the Scope = 4 we are stating that 1X is going to look over four candles for the high/low range.
The Scope property is used to determine how many candles it is to scan to determine the high/low range for the corresponding 1X, 3X, 5X and 10X periods. This is how different time ranges are put into perspective. Using a 3M chart with Scope = 4 would represent the following time windows:
- 1X = 3M * 4 is a 12 Months or 1 Year High/Low Range
- 3X = 3M * 4 * 3 is a 36 Months or 3 Years High/Low Range
- 5X = 3M * 4 * 5 is a 60 Months or 5 Years High/Low Range
- 10X = 3M * 4 * 10 is a 120 Months or 10 Years High/Low Range.
With these calculations, the indicator then determines where current price is within each of these High/Low ranges from a percentage perspective between 0% and 100%.
Once the 0% to 100% value is calculated, it then will shade the value according to a color gradient from red to green (or any other two colors you set the indictor to). This color shading really helps to interpret current price quickly.
The greater power to this range and color shading comes when you are able to see where price is according to price history across the multiple time windows. In this example, there is quick analysis across 1 Year, 3 Year, 5 Year and 10 Year windows.
Now let's further improve this quick analysis over 15 different stocks for which the indicator allows you to watch up to at any one time.
For value traders this is huge, because we're always looking for the bargains and we wait for price to be in the value range. Using this indicator helps to instantly see if price has entered a value range before we decide to do further analysis with other charting and fundamental tools.
The Code
The heart of all this is really very simple as you can see in the following code snippet. We're simply looking for the highest high and lowest low across the different scopes and calculating the percentage of the range where current price is for each symbol being watched.
scope = baseScope
watch1X = math.round(((watchClose - ta.lowest(watchLow, scope)) / (ta.highest(watchHigh, scope) - ta.lowest(watchLow, scope))) * 100, 0)
table.cell(tblWatch, columnId, 2, str.format("{0, number, #}%", watch1X), text_size = size.small, text_color = colorText, bgcolor = getBackColor(watch1X))
//3X Lookback
scope := baseScope * 3
watch3X = math.round(((watchClose - ta.lowest(watchLow, scope)) / (ta.highest(watchHigh, scope) - ta.lowest(watchLow, scope))) * 100, 0)
table.cell(tblWatch, columnId, 3, str.format("{0, number, #}%", watch3X), text_size = size.small, text_color = colorText, bgcolor = getBackColor(watch3X))
Conclusion
The example I've laid out here are for large time windows, because I'm a long term investor. However, keep in mind that this can work on any chart setting, you just need to remember that your chart's time period and scope work together to determine what 1X, 3X, 5X and 10X represent.
Let me try and give you one last scenario on this. Consider your chart is set for a 60 minute chart, meaning each candle represents 60 minutes of time and you set the Stock Watch indicator to a scope = 4. These settings would now represent the following and you would be watching up to 15 different stocks across these windows at one time.
1X = 60 minutes * 4 is 240 minutes or 4 hours of time.
3X = 60 minutes * 4 * 3 = 720 minutes or 12 hours of time.
5X = 60 minutes * 4 * 5 = 1200 minutes or 20 hours of time.
10X = 60 minutes * 4 * 10 = 2400 minutes or 40 hours of time.
I hope you find value in my contribution to the cause of trading, and if you have any comments or critiques, I would love to here from you in the comments.
STD-Filtered, Variety FIR Digital Filters w/ ATR Bands [Loxx]STD-Filtered, Variety FIR Digital Filters w/ ATR Bands is a FIR Digital Filter indicator with ATR bands. This indicator contains 12 different digital filters. Some of these have already been covered by indicators that I've recently posted. The difference here is that this indicator has ATR bands, allows for frequency filtering, adds a frequency multiplier, and attempts show causality by lagging price input by 1/2 the period input during final application of weights. Period is restricted to even numbers.
The 3 most important parameters are the frequency cutoff, the filter window type and the "causal" parameter.
Included filter types:
- Hamming
- Hanning
- Blackman
- Blackman Harris
- Blackman Nutall
- Nutall
- Bartlet Zero End Points
- Bartlet Hann
- Hann
- Sine
- Lanczos
- Flat Top
Frequency cutoff can vary between 0 and 0.5. General rule is that the greater the cutoff is the "faster" the filter is, and the smaller the cutoff is the smoother the filter is.
You can read more about discrete-time signal processing and some of the windowing functions in this indicator here:
Window function
Window Functions and Their Applications in Signal Processing
What are FIR Filters?
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages.
A finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying).
The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero.
FIR filters can be discrete-time or continuous-time, and digital or analog.
A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed.
An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight.
What is a Standard Deviation Filter?
If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering.
Included
Bar coloring
Loxx's Expanded Source Types
Signals
Alerts
Related indicators
STD/C-Filtered, N-Order Power-of-Cosine FIR Filter
STD/C-Filtered, Power-of-Cosine FIR Filter
STD/C-Filtered, Truncated Taylor Family FIR Filter
STD/Clutter-Filtered, Variety FIR Filters
STD/Clutter-Filtered, Kaiser Window FIR Digital Filter
