inverse_fisher_transform_adaptive_stochastic█ Description
The indicator is the implementation of inverse fisher transform an indicator transform of the adaptive stochastic (dominant cycle), as in the Cycle Analytics for Trader pg. 198 (John F. Ehlers). Indicator transformation in brief means reshaping the indicator to be more interpretable. The inverse fisher transform is achieved by compressing values near the extremes many extraneous and irrelevant wiggles are removed from the indicator, as cited.
█ Inverse Fisher Transform
input = 2*(adaptive_stoc - .5)
output = e(2*k*input) -1 / e(2*k*input) +1
█ Feature:
iFish i.e. output value
trigger i.e. previous 1 bar of iFish * 0.90
if iFish crosses above the trigger, consider a buy indicated with the green line
while, iFish crosses below the trigger, consider a sell indicate by the red line
in addition iFish needs to be greater than the previous iFish
在腳本中搜尋"Cycle"
timing marketIntraday time cycle . it is valid for nifty and banknifty .just add this on daily basis . ignore previous day data
BTC Pi MultipleThe Pi Multiple is a function of 350 and 111-day moving average. When both intersect and the 111-day MA crosses above, it has historically coincided with a cycle top with a 3-day margin.
With the Pi Multiple, this intersection is visible when the line crosses zero upwards.
The indicator is called the Pi Multiple because 350/111 is close to Pi. It is based on the Pi Cycle Top Indicator developed by Philip Swift and has been modified for better readability by David Bertho.
Bitcoin Fundamentals - Puell MultipleThis is an indicator that derives from Bitcoin Mining daily generated Income.
It does show a perfect track record on calling Bitcoin cycle tops and cycle bottoms.
For those of you willing to experiment, I've enabled the ability to set custom periods (365 by default).
The indicator includes custom alerts to notify the entry and the exit from OverBought (OB) & OverSold (OS) bands.
Credits: David Puell twitter.com
Cycle Dynamic Composite AverageThis MA uses the formula of simple cycle indicator to find 2 cycles periods length's .
The CDCA is the result of 8 different ma to control and filter the price. The regression line is the signal , don t need to look candles, but just the cross between MA and reg lin.
Election Year GainsShows the yearly gains of the chart in U.S. Election years.
Use the options to turn on other years in the cycle.
For use with the 12M chart.
Will show non-sensical data with other intervals.
TASC 2025.06 Cybernetic Oscillator█ OVERVIEW
This script implements the Cybernetic Oscillator introduced by John F. Ehlers in his article "The Cybernetic Oscillator For More Flexibility, Making A Better Oscillator" from the June 2025 edition of the TASC Traders' Tips . It cascades two-pole highpass and lowpass filters, then scales the result by its root mean square (RMS) to create a flexible normalized oscillator that responds to a customizable frequency range for different trading styles.
█ CONCEPTS
Oscillators are indicators widely used by technical traders. These indicators swing above and below a center value, emphasizing cyclic movements within a frequency range. In his article, Ehlers explains that all oscillators share a common characteristic: their calculations involve computing differences . The reliance on differences is what causes these indicators to oscillate about a central point.
The difference between two data points in a series acts as a highpass filter — it allows high frequencies (short wavelengths) to pass through while significantly attenuating low frequencies (long wavelengths). Ehlers demonstrates that a simple difference calculation attenuates lower-frequency cycles at a rate of 6 dB per octave. However, the difference also significantly amplifies cycles near the shortest observable wavelength, making the result appear noisier than the original series. To mitigate the effects of noise in a differenced series, oscillators typically smooth the series with a lowpass filter, such as a moving average.
Ehlers highlights an underlying issue with smoothing differenced data to create oscillators. He postulates that market data statistically follows a pink spectrum , where the amplitudes of cyclic components in the data are approximately directly proportional to the underlying periods. Specifically, he suggests that cyclic amplitude increases by 6 dB per octave of wavelength.
Because some conventional oscillators, such as RSI, use differencing calculations that attenuate cycles by only 6 dB per octave, and market cycles increase in amplitude by 6 dB per octave, such calculations do not have a tangible net effect on larger wavelengths in the analyzed data. The influence of larger wavelengths can be especially problematic when using these oscillators for mean reversion or swing signals. For instance, an expected reversion to the mean might be erroneous because oscillator's mean might significantly deviate from its center over time.
To address the issues with conventional oscillator responses, Ehlers created a new indicator dubbed the Cybernetic Oscillator. It uses a simple combination of highpass and lowpass filters to emphasize a specific range of frequencies in the market data, then normalizes the result based on RMS. The process is as follows:
Apply a two-pole highpass filter to the data. This filter's critical period defines the longest wavelength in the oscillator's passband.
Apply a two-pole SuperSmoother (lowpass filter) to the highpass-filtered data. This filter's critical period defines the shortest wavelength in the passband.
Scale the resulting waveform by its RMS. If the filtered waveform follows a normal distribution, the scaled result represents amplitude in standard deviations.
The oscillator's two-pole filters attenuate cycles outside the desired frequency range by 12 dB per octave. This rate outweighs the apparent rate of amplitude increase for successively longer market cycles (6 dB per octave). Therefore, the Cybernetic Oscillator provides a more robust isolation of cyclic content than conventional oscillators. Best of all, traders can set the periods of the highpass and lowpass filters separately, enabling fine-tuning of the frequency range for different trading styles.
█ USAGE
The "Highpass period" input in the "Settings/Inputs" tab specifies the longest wavelength in the oscillator's passband, and the "Lowpass period" input defines the shortest wavelength. The oscillator becomes more responsive to rapid movements with a smaller lowpass period. Conversely, it becomes more sensitive to trends with a larger highpass period. Ehlers recommends setting the smallest period to a value above 8 to avoid aliasing. The highpass period must not be smaller than the lowpass period. Otherwise, it causes a runtime error.
The "RMS length" input determines the number of bars in the RMS calculation that the indicator uses to normalize the filtered result.
This indicator also features two distinct display styles, which users can toggle with the "Display style" input. With the "Trend" style enabled, the indicator plots the oscillator with one of two colors based on whether its value is above or below zero. With the "Threshold" style enabled, it plots the oscillator as a gray line and highlights overbought and oversold areas based on the user-specified threshold.
Below, we show two instances of the script with different settings on an equities chart. The first uses the "Threshold" style with default settings to pass cycles between 20 and 30 bars for mean reversion signals. The second uses a larger highpass period of 250 bars and the "Trend" style to visualize trends based on cycles spanning less than one year:
Higher Timeframe MACD blocks w/ compressed histogramThe example above plots MACD and HTF MACD for reference.
This innovative MACD display combine MACD + Histogram + HTF (higher TImeframe) MACD all in one plot thanks to a colored band and clever histogram numbering.
All MACD in a blink of an eye !
Transparent blocks : not aligned with HTF
Opaque blocks : aligned with HTF
Color code (4 colors, full cycle) :
Yellow -> MACD > SIGNAL, below 0
Green -> MACD > SIGNAL, above 0
Purple -> MACD < SIGNAL, above 0
Red -> MACD < SIGNAL, below 0
Histogram meaning :
Numbers above the main plots represent the cumulative trend from the histogram, green is up, red is down. The minimum is 1 and the maximum is 9 (due to limitation from trading view, the MACD histogram rarely go above 9 anyway).
Explanation: when MACD and SIGNAL lines are about the same histogram count is around 1 and vice versa.
Choose your own MACD length and HTF with this indicator settings.
SignalState990 - Mood & Cycle OverlayClean structure
Noise filtering
Multi-timeframe logic
Clear visual states
Volume Cycle TrackerThis indicator measures the average bar-to-bar distance between recent high-volume candles, defined as candles with volume greater than its own 20-period SMA. The less frequent the high-volume candles, the higher the output value, helping visualize periods of reduced strong participation. It’s useful for identifying expansions and contractions in volume pressure without relying on raw volume bars. The values are smoothed to reduce noise. Can be used to filter out weak consolidations or spot re-accumulation zones.
XRP Breathe Strategy Zones🫁 XRP Breathe Strategy Zones
A time-based trading overlay designed specifically for XRPUSD.
This tool highlights weekly "Inhale" and "Exhale" phases based on a 20-day cycle of price action. It visually guides traders through expected accumulation and distribution zones, helping align trades with market rhythm.
🔹 Key Features:
Color-coded Inhale and Exhale phases
Critical price levels marked for support and resistance
Built-in signal arrows for trend confirmation
Perfect for swing traders and intraday strategists looking to trade XRP with more structure, timing, and confidence.
JCICT - ModelThe Unicorn model—an FVG (Fair Value Gap) nested within a breaker block—is one of the strongest algorithmic entry setups, often occurring after liquidity is taken at the opening price. Within the MMXM (Market Maker X Model) framework, this model typically forms after a phase of distribution or accumulation that aligns with the structured session cycle (Asia–London–New York). Notably, when a Unicorn setup forms after the Asian session—which usually consolidates or accumulates liquidity—it signals a high probability for reversal going into the London or New York sessions.
By applying a multiple time frame narrative, traders can align higher time frame bias (e.g., bullish on the Daily or H4) with lower time frame structures (such as M15–M5), where a breaker and FVG align. When price displaces through and reclaims the breaker block with strong impulse, it indicates that liquidity has been taken and the market is ready to move in the opposite direction. This is where the ICT methodology thrives—by seeking reversal points through liquidity manipulation rather than trend continuation.
If this model appears during killzones like the London Open or New York Open, and liquidity has been taken around the daily open, it significantly strengthens the probability of a high-quality reversal trade. Therefore, the Unicorn model is not merely a technical structure—it reflects a deeper narrative of smart money manipulation across sessions, confirmed by top-down bias and price action context.
MacroHeat (Global Macro Growth Proxy)Overview:
MacroHeat by CWRP is a proprietary macroeconomic sentiment indicator that tracks the temperature of global industrial and risk-linked activity using market-based signals. It distills asset movements from metals, foreign exchange, and energy markets into a single, smoothed composite value. This tool is designed to help portfolio managers, traders, and strategists gauge the direction and momentum of real economy growth expectations.
MacroHeat does not predict policy or price action directly—it measures macro risk appetite and industrial growth expectations across three crucial asset pairs:
Copper/Gold Ratio – Industrial Metals vs. Defensive Metal
AUD/JPY Cross – Commodity-sensitive FX vs. Safe-haven FX
Brent/NatGas Ratio – Oil Demand vs. Gas Oversupply
These inputs are transformed into standardized z-scores to generate an intuitive composite signal of expansion, contraction, or neutrality in the global growth regime
Interpretation:
Copper / Gold Ratio
Copper is widely used in construction, manufacturing, and infrastructure. It responds to real-world industrial activity.
Gold is a traditional safe-haven asset, bid up in times of uncertainty or deflationary pressure. A rising Copper/Gold ratio implies higher industrial activity relative to defensive hedging, consistent with expansionary conditions.
AUD / JPY
AUD (Australian Dollar) is closely tied to the commodity cycle and heavily exposed to Chinese demand, especially for raw materials like iron ore and coal. JPY (Japanese Yen) is a low yielding, defensive currency that tends to strengthen during global stress due to Japan’s net external creditor position. A rising AUD/JPY indicates risk on sentiment and strength in Chinese or regional industrial demand. Falling values may signal risk aversion or cooling commodity linked activity.
📌 *Note: AUD is a proxy for China linked global demand. JPY reflects broader global risk sentiment, not the Japanese economy per se.
Brent / NatGas Ratio
Brent crude prices reflect global oil demand, typically linked to transportation, logistics, and industrial usage. Natural Gas, though also industrial, is often supply heavy and regionally priced. A high Brent/NatGas ratio can indicate tight oil supply or strong demand, relative to gas, suggesting higher economic activity.
------------------------------------------------------------------------------------------------------------
Each of the above components is converted into a Z-score using log returns over a 252-day rolling window. This standardizes movement and allows for cross-market comparison. The indicator then:
Averages the Z-scores of the three components (>1 is expansive, <-1 is contractive)
Smooths the result using a 5-day simple moving average
Classifies the result into macroeconomic regimes
And outputs to the table which has live component Z-scores with visual cues (yellow = expansionary; blue = contractionary).
Thank you for using the Global Macro Growth Proxy by CWRP!
I'm open to all critiques and discussion around macroeconomics and hope you find use in this model!
QT Separator by BailaSimple and Clean QT indicator.
Helps to spot SSMT
Based on: Daye Quarterly Theory by toodegrees
These Quarters represent:
A - Accumulation (required for a cycle to occur)
M - Manipulation
D - Distribution
X - Reversal/Continuation
Time Block with Current K-Line TimeTiltle:
Time Block and Current K-line Time
Core Functions:
1. This indicator provides traders with a powerful time analysis tool to help identify key time nodes and market structures. Generally speaking, the duration of a market trend is a time block
2. Multiple time zone support, supporting five major trading time zones: Shanghai, New York, London, Tokyo, and UTC, and adaptive time display in the selected time zone
3. Time block visualization: select the time block length according to the observation period, and draw a separator line at the time block boundary
4. Real-time time display: current K-line detailed time (year/month/day hour: minute week)
5. Future time prediction, the next time block starts at the future dividing line, and the countdown function displays the time to the next block, which is used to assist in judging the remaining duration of the current trend
Usage Scenarios:
Day trading: Identify trading day boundaries (1-day blocks)
Swing trading: Grasp the weekly/monthly time frame conversion (1-week/1-month blocks)
Long-term investment: Observe the annual market cycle (1-year blocks)
Cross-time zone trading: Seamlessly switch between major global trading time zones
——————————————————————————————————————————————————————————
标题：
时间区块与当前K线时间
核心功能：
1. 本指标为交易者提供强大的时间分析工具，帮助识别关键时间节点和市场结构，通常而言，一段行情持续的时间为一个时间区块
2. 多时区支持，支持上海、纽约、伦敦、东京、UTC五大交易时区，自适应所选时区的时间显示
3. 时间区块可视化：根据观测周期选择时间区块长度，在时间区块边界绘制分隔线
4. 实时时间显示：当前K线详细时间（年/月/日 时:分 星期）
5. 未来时间预测，下一个时间区块开始位置显示未来分割线，倒计时功能显示距离下个区块的时间，用于辅助判断当前趋势的剩余持续时间
使用场景：
日内交易：识别交易日边界（1日区块）
波段交易：把握周/月时间框架转换（1周/1月区块）
长期投资：观察年度市场周期（1年区块）
跨时区交易：无缝切换全球主要交易时区
zSph x Larry Waves Wave Degree TimingElliott Waves are fractal structures governed by time. The categorization of time in relation to Elliott Wave is named ‘Wave Degree’.
All waves are characterized by relative size called degree. The degree of a wave is determined by its size and position relative to lesser waves (smaller time and size), corresponding waves (similar time and size) and encompassing waves (greater time and size).
Elliott named 9 degrees (Supercycle – Subminuette).
Elliott also stated the Subminuette degree is discernable on the HOURLY chart.
# Concept
BINANCE:BTCUSDT
Degree is governed by Time yet it is not based upon time lengths (or price lengths), rather it is based on form and structure – a function of both price and time.
The precise degree may not be identified in real time, yet the objective is to be within +/- 1 standard deviation of the expected degree to be aware of the overall market progression.
Understanding degree helps in the identification of when an impulse or a correction is nearing completion and to be aware of the major pivot in price action to occur as a result of the completion of a major expansion or major retracement and be aware of when major pivots in price relating to major expansions and major retracements by managing expectations from a time perspective.
*Important to understand* : If price is currently in a Wave Degree Extension or a Very Complex Correction, the wave degree timings will be distorted (extended in time).
Example: A Cycle typically lasts a few years - yet can last a decade(s) in an Extension.
It’s best to keep the analysis on the Minute/Minuette timeframe to manage timing expectations yet always refer back to the Higher Time Frame Structure.***
# Correct Usage
BEFORE PLACING THE ANCHOR TO DISPLAY ZONES:
Completion of prior wave structure should be completed and there needs to be confirmation the next wave structure is in progression, such as a change in market structure.
Anchor :
Best to anchor on the higher time frame to ensure you always have the anchor point defined when you scale down/move down in the timeframes.
Ensure the anchor point is placed at the termination of a structure/beginning of a new structure (Generally they will be price extremes – extreme highs and lows)
Zones :
Minimum Zones : The minimum amount of time of completion for a single wave structure to complete for a degree.
Average Zones : The average amount of time of completion for a single wave structure to complete for a degree.
Maximum Zones : The general maximum amount of time of completion for a single wave structure to complete for a degree.
Wave Degree Timeframe Analysis :
Higher-Level Degrees (Primary, Intermediate, Minor) - Utilize on H4+ timeframe
Lower-Level Degrees (Minute, Minuette, Subminuette) – Utilize on 15M to H4 timeframe
Micro-Level Degrees (Micro and Submicro) – Utilize on timeframes less than 15M
(There is a chart in the settings you can toggle on/off that reiterates this as well.)
# Settings
Y-Axis Offset :
It is a scale relative to the asset being viewed. Example:
- If using on Bitcoin, Bitcoin moves on average $1,000 of dollars up or down (on the Y-Axis), therefore it would be relevant to use values with 4 nominal values to offset it correctly to view easier on the chart as needed.
- If using on SP500, SP500 moves on average $50-100 of dollars up or down (on the Y-Axis), therefore it would be relevant to use values with 2 or 3 nominal values to offset it correctly to view easier on the chart as needed.
Extend :
This option allows to extend lines for the borders of the zones towards price action.
z-score-calkusi-v1.143z-scores incorporate the moment of N look-back bars to allow future price projection.
z-score = (X - mean)/std.deviation ; X = close
z-scores update with each new close print and with each new bar. Each new bar augments the mean and std.deviation for the N bars considered. The old Nth bar falls away from consideration with each new historical bar.
The indicator allows two other options for X: RSI or Moving Average.
NOTE: While trading use the "price" option only.
The other two options are provided for visualisation of RSI and Moving Average as z-score curves.
Use z-scores to identify tops and bottoms in the future as well as intermediate intersections through which a z-score will pass through with each new close and each new bar.
Draw lines from peaks and troughs in the past through intermediate peaks and troughs to identify projected intersections in the future. The most likely intersections are those that are formed from a line that comes from a peak in the past and another line that comes from a trough in the past. Try getting at least two lines from historical peaks and two lines from historical troughs to pass through a future intersection.
Compute the target intersection price in the future by clicking on the z-score indicator header to see a drag-able horizontal line to drag over the intersection. The target price is the last value displayed in the indicator's status bar after the closing price.
When the indicator header is clicked, a white horizontal drag-able line will appear to allow dragging the line over an intersection that has been drawn on the indicator for a future z-score projection and the associated future closing price.
With each new bar that appears, it is necessary to repeat the procedure of clicking the z-score indicator header to be able to drag the drag-able horizontal line to see the new target price for the selected intersection. The projected price will be different from the current close price providing a price arbitrage in time.
New intermediate peaks and troughs that appear require new lines be drawn from the past through the new intermediate peak to find a new intersection in the future and a new projected price. Since z-score curves are sort of cyclical in nature, it is possible to see where one has to locate a future intersection by drawing lines from past peaks and troughs.
Do not get fixated on any one projected price as the market decides which projected price will be realised. All prospective targets should be manually updated with each new bar.
When the z-score plot moves outside a channel comprised of lines that are drawn from the past, be ready to adjust to new market conditions.
z-score plots that move above the zero line indicate price action that is either rising or ranging. Similarly, z-score plots that move below the zero line indicate price action that is either falling or ranging. Be ready to adjust to new market conditions when z-scores move back and forth across the zero line.
A bar with highest absolute z-score for a cycle screams "reversal approaching" and is followed by a bar with a lower absolute z-score where close price tops and bottoms are realised. This can occur either on the next bar or a few bars later.
The indicator also displays the required N for a Normal(0,1) distribution that can be set for finer granularity for the z-score curve.This works with the Confidence Interval (CI) z-score setting. The default z-score is 1.96 for 95% CI.
Common Confidence Interval z-scores to find N for Normal(0,1) with a Margin of Error (MOE) of 1:
70% 1.036
75% 1.150
80% 1.282
85% 1.440
90% 1.645
95% 1.960
98% 2.326
99% 2.576
99.5% 2.807
99.9% 3.291
99.99% 3.891
99.999% 4.417
9-Jun-2025
Added a feature to display price projection labels at z-score levels 3, 2, 1, 0, -1, -2, 3.
This provides a range for prices available at the current time to help decide whether it is worth entering a trade. If the range of prices from say z=|2| to z=|1| is too narrow, then a trade at the current time may not be worth the risk.
Added plot for z-score moving average.
28-Jun-2025
Added Settings option for # of Std.Deviation level Price Labels to display. The default is 3. Min is 2. Max is 6.
This feature allows likelihood assessment for Fibonacci price projections from higher time frames at lower time frames. A Fibonacci price projection that falls outside |3.x| Std.Deviations is not likely.
Added Settings option for Chart Bar Count and Target Label Offset to allow placement of price labels for the standard z-score levels to the right of the window so that these are still visible in the window.
Target Label Offset allows adjustment of placement of Target Price Label in cases when the Target Price Label is either obscured by the price labels for the standard z-score levels or is too far right to be visible in the window.
9-Jul-2025
z-score 1.142 updates:
Displays in the status line before the close price the range for the selected Std. Deviation levels specified in Settings and |z-zMa|.
When |z-zMa| > |avg(z-zMa)| and zMa rising, |z-zMa| and zMa displays in aqua.
When |z-zMa| > |avg(z-zMa)| and zMa falling, |z-zMa| and zMa displays in red.
When |z-zMa| <= |avg(z-zMa)|, z and zMa display in gray.
z usually crosses over zMa when zMa is gray but not always. So if cross-over occurs when zMa is not gray, it implies a strong move in progress.
Practice makes perfect.
Use this indicator at your own risk
HIFI BTC Daily Hashrate Momentum OscillatorThe "HIFI BTC Daily Hashrate Momentum Oscillator" indicator is an oscillator that analyzes the "health" and confidence of miners in the Bitcoin network. It measures the momentum of hashrate changes using its deviation from the 30-day and 60-day moving averages. A rising hashrate is often a leading or confirming bullish trend indicator for the price of BTC.
Main Idea
Hashrate is the total computing power involved in mining. Its growth indicates increased investment in network security and miners' confidence in future profitability.
Blue Oscillator (fast): Shows the short-term dynamics of hashrate growth.
Green Oscillator (slow): Indicates the long-term trend of hash rate changes.
Chart background: The green background signals the acceleration of the hash rate growth (short-term momentum is higher than long-term), which is a positive sign.
How to Read Signals
A Buy signal appears when two fundamental conditions coincide:
Growth acceleration: The short-term hashrate momentum becomes stronger than the long-term one (the blue line crosses the green one from bottom to top). This indicates that miners are actively building capacity.
Exit from stagnation: This acceleration occurs after a period of weak hashrate growth or decline (the green line is below the red dashed line).
This combination indicates the potential start of a new cycle of growth and confidence in the network, which historically has often preceded the rise in the price of Bitcoin itself.
Disclamer: This indicator is an analysis tool and should not be considered as a direct financial recommendation. Always do your own analysis before making trades.
Omori Law Recovery PhasesWhat is the Omori Law?
Originally a seismological model, the Omori Law describes how earthquake aftershocks decay over time. It follows a power law relationship: the frequency of aftershocks decreases roughly proportionally to 1/(t+c)^p, where:
t = time since the main shock
c = time offset constant
p = power law exponent (typically around 1.0)
Application to the markets
Financial markets experience "aftershocks" similar to earthquakes:
Market Crashes as Main Shocks: Major market declines (crashes) represent the initial shock event.
Volatility Decay: After a crash, market volatility typically declines following a power law pattern rather than a linear or exponential one.
Behavioral Components: The decay pattern reflects collective market psychology - initial panic gives way to uncertainty, then stabilization, and finally normalization.
The Four Recovery Phases
The Omori decay pattern in markets can be divided into distinct phases:
Acute Phase: Immediately after the crash, characterized by extreme volatility, panic selling, and sharp reversals. Trading is hazardous.
Reaction Phase: Volatility begins decreasing, but markets test previous levels. False rallies and retests of lows are common.
Repair Phase: Structure returns to the market. Volatility approaches normal levels, and traditional technical analysis becomes more reliable.
Recovery Phase: The final stage where market behavior normalizes completely. The impact of the original shock has fully decayed.
Why It Matters for Traders
Understanding where the market stands in this recovery cycle provides valuable context:
Risk Management: Adjust position sizing based on the current phase
Strategy Selection: Different strategies work in different phases
Psychological Preparation: Know what to expect based on the phase
Time Horizon Guidance: Each phase suggests appropriate time frames for trading
z-score-calkusi-v1.14z-scores incorporate the moment of N look-back bars to allow future price projection.
z-score = (X - mean)/std.deviation ; X = close
z-scores update with each new close print and with each new bar. Each new bar augments the mean and std.deviation for the N bars considered. The old Nth bar falls away from consideration with each new historical bar.
The indicator allows two other options for X: RSI or Moving Average.
NOTE: While trading use the "price" option only.
The other two options are provided for visualisation of RSI and Moving Average as z-score curves.
Use z-scores to identify tops and bottoms in the future as well as intermediate intersections through which a z-score will pass through with each new close and each new bar.
Draw lines from peaks and troughs in the past through intermediate peaks and troughs to identify projected intersections in the future. The most likely intersections are those that are formed from a line that comes from a peak in the past and another line that comes from a trough in the past. Try getting at least two lines from historical peaks and two lines from historical troughs to pass through a future intersection.
Compute the target intersection price in the future by clicking on the z-score indicator header to see a drag-able horizontal line to drag over the intersection. The target price is the last value displayed in the indicator's status bar after the closing price.
When the indicator header is clicked, a white horizontal drag-able line will appear to allow dragging the line over an intersection that has been drawn on the indicator for a future z-score projection and the associated future closing price.
With each new bar that appears, it is necessary to repeat the procedure of clicking the z-score indicator header to be able to drag the drag-able horizontal line to see the new target price for the selected intersection. The projected price will be different from the current close price providing a price arbitrage in time.
New intermediate peaks and troughs that appear require new lines be drawn from the past through the new intermediate peak to find a new intersection in the future and a new projected price. Since z-score curves are sort of cyclical in nature, it is possible to see where one has to locate a future intersection by drawing lines from past peaks and troughs.
Do not get fixated on any one projected price as the market decides which projected price will be realised. All prospective targets should be manually updated with each new bar.
When the z-score plot moves outside a channel comprised of lines that are drawn from the past, be ready to adjust to new market conditions.
z-score plots that move above the zero line indicate price action that is either rising or ranging. Similarly, z-score plots that move below the zero line indicate price action that is either falling or ranging. Be ready to adjust to new market conditions when z-scores move back and forth across the zero line.
A bar with highest absolute z-score for a cycle screams "reversal approaching" and is followed by a bar with a lower absolute z-score where close price tops and bottoms are realised. This can occur either on the next bar or a few bars later.
The indicator also displays the required N for a Normal(0,1) distribution that can be set for finer granularity for the z-score curve.This works with the Confidence Interval (CI) z-score setting. The default z-score is 1.96 for 95% CI.
Common Confidence Interval z-scores to find N for Normal(0,1) with a Margin of Error (MOE) of 1:
70% 1.036
75% 1.150
80% 1.282
85% 1.440
90% 1.645
95% 1.960
98% 2.326
99% 2.576
99.5% 2.807
99.9% 3.291
99.99% 3.891
99.999% 4.417
9-Jun-2025
Added a feature to display price projection labels at z-score levels 3, 2, 1, 0, -1, -2, 3.
This provides a range for prices available at the current time to help decide whether it is worth entering a trade. If the range of prices from say z=|2| to z=|1| is too narrow, then a trade at the current time may not be worth the risk.
Added plot for z-score moving average.
28-Jun-2025
Added Settings option for # of Std.Deviation level Price Labels to display. The default is 3. Min is 2. Max is 6.
This feature allows likelihood assessment for Fibonacci price projections from higher time frames at lower time frames. A Fibonacci price projection that falls outside |3.x| Std.Deviations is not likely.
Added Settings option for Chart Bar Count and Target Label Offset to allow placement of price labels for the standard z-score levels to the right of the window so that these are still visible in the window.
Target Label Offset allows adjustment of placement of Target Price Label in cases when the Target Price Label is either obscured by the price labels for the standard z-score levels or is too far right to be visible in the window.
Practice makes perfect.
Use this indicator at your own risk
QG-Particle OscillatorThis is an advanced oscillator based on auxiliary particle filter. It separates signal from noise and uses smoothing algorithm similar to JMA.
The main oscillator line is a smoothed and detrended version of the price series similar to detrended oscillator line. The purple/aqua lines are a prediction based on an additional adaptive smoothing technique and current volatility.
The prediction is smoothed twice and is supposed to represent the true signal without any noise, thus the prediction should always be less than the raw detrend line. However, certain volatile conditions will cause the prediction to cross above/below the detrend line. When this happens the likelihood of a reversal or pullback is extremely high.
There are 3 dots on the zero line- Red, Green and Yellow. The yellow dots warn of an eminent pullback 2 bars before it actually occurs. This is a non-repainting indicator.
One can also use this indicator to trade CCI signals, similar to zero line rejection in existing trend.
The indicator has 2 settings- Period and Phase. The phase represents cycle phase and Period represents oscillator period.
Credits: This indicator has been originally published for Ninjatrader and this is conversion into pinescript.
Lyapunov Market Instability (LMI)Lyapunov Market Instability (LMI)
What is Lyapunov Market Instability?
Lyapunov Market Instability (LMI) is a revolutionary indicator that brings chaos theory from theoretical physics into practical trading. By calculating Lyapunov exponents—a measure of how rapidly nearby trajectories diverge in phase space—LMI quantifies market sensitivity to initial conditions. This isn't another oscillator or trend indicator; it's a mathematical lens that reveals whether markets are in chaotic (trending) or stable (ranging) regimes.
Inspired by the meditative color field paintings of Mark Rothko, this indicator transforms complex chaos mathematics into an intuitive visual experience. The elegant simplicity of the visualization belies the sophisticated theory underneath—just as Rothko's seemingly simple color blocks contain profound depth.
Theoretical Foundation (Chaos Theory & Lyapunov Exponents)
In dynamical systems, the Lyapunov exponent (λ) measures the rate of separation of infinitesimally close trajectories:
λ > 0: System is chaotic—small changes lead to dramatically different outcomes (butterfly effect)
λ < 0: System is stable—trajectories converge, perturbations die out
λ ≈ 0: Edge of chaos—transition between regimes
Phase Space Reconstruction
Using Takens' embedding theorem , we reconstruct market dynamics in higher dimensions:
Time-delay embedding: Create vectors from price at different lags
Nearest neighbor search: Find historically similar market states
Trajectory evolution: Track how these similar states diverged over time
Divergence rate: Calculate average exponential separation
Market Application
Chaotic markets (λ > threshold): Strong trends emerge, momentum dominates, use breakout strategies
Stable markets (λ < threshold): Mean reversion dominates, fade extremes, range-bound strategies work
Transition zones: Market regime about to change, reduce position size, wait for confirmation
How LMI Works
1. Phase Space Construction
Each point in time is embedded as a vector using historical prices at specific delays (τ). This reveals the market's hidden attractor structure.
2. Lyapunov Calculation
For each current state, we:
- Find similar historical states within epsilon (ε) distance
- Track how these initially similar states evolved
- Measure exponential divergence rate
- Average across multiple trajectories for robustness
3. Signal Generation
Chaos signals: When λ crosses above threshold, market enters trending regime
Stability signals: When λ crosses below threshold, market enters ranging regime
Divergence detection: Price/Lyapunov divergences signal potential reversals
4. Rothko Visualization
Color fields: Background zones represent market states with Rothko-inspired palettes
Glowing line: Lyapunov exponent with intensity reflecting market state
Minimalist design: Focus on essential information without clutter
Inputs:
📐 Lyapunov Parameters
Embedding Dimension (default: 3)
Dimensions for phase space reconstruction
2-3: Simple dynamics (crypto/forex) - captures basic momentum patterns
4-5: Complex dynamics (stocks/indices) - captures intricate market structures
Higher dimensions need exponentially more data but reveal deeper patterns
Time Delay τ (default: 1)
Lag between phase space coordinates
1: High-frequency (1m-15m charts) - captures rapid market shifts
2-3: Medium frequency (1H-4H) - balances noise and signal
4-5: Low frequency (Daily+) - focuses on major regime changes
Match to your timeframe's natural cycle
Initial Separation ε (default: 0.001)
Neighborhood size for finding similar states
0.0001-0.0005: Highly liquid markets (major forex pairs)
0.0005-0.002: Normal markets (large-cap stocks)
0.002-0.01: Volatile markets (crypto, small-caps)
Smaller = more sensitive to chaos onset
Evolution Steps (default: 10)
How far to track trajectory divergence
5-10: Fast signals for scalping - quick regime detection
10-20: Balanced for day trading - reliable signals
20-30: Slow signals for swing trading - major regime shifts only
Nearest Neighbors (default: 5)
Phase space points for averaging
3-4: Noisy/fast markets - adapts quickly
5-6: Balanced (recommended) - smooth yet responsive
7-10: Smooth/slow markets - very stable signals
📊 Signal Parameters
Chaos Threshold (default: 0.05)
Lyapunov value above which market is chaotic
0.01-0.03: Sensitive - more chaos signals, earlier detection
0.05: Balanced - optimal for most markets
0.1-0.2: Conservative - only strong trends trigger
Stability Threshold (default: -0.05)
Lyapunov value below which market is stable
-0.01 to -0.03: Sensitive - quick stability detection
-0.05: Balanced - reliable ranging signals
-0.1 to -0.2: Conservative - only deep stability
Signal Smoothing (default: 3)
EMA period for noise reduction
1-2: Raw signals for experienced traders
3-5: Balanced - recommended for most
6-10: Very smooth for position traders
🎨 Rothko Visualization
Rothko Classic: Deep reds for chaos, midnight blues for stability
Orange/Red: Warm sunset tones throughout
Blue/Black: Cool, meditative ocean depths
Purple/Grey: Subtle, sophisticated palette
Visual Options:
Market Zones : Background fields showing regime areas
Transitions: Arrows marking regime changes
Divergences: Labels for price/Lyapunov divergences
Dashboard: Real-time state and trading signals
Guide: Educational panel explaining the theory
Visual Logic & Interpretation
Main Elements
Lyapunov Line: The heart of the indicator
Above chaos threshold: Market is trending, follow momentum
Below stability threshold: Market is ranging, fade extremes
Between thresholds: Transition zone, reduce risk
Background Zones: Rothko-inspired color fields
Red zone: Chaotic regime (trending)
Gray zone: Transition (uncertain)
Blue zone: Stable regime (ranging)
Transition Markers:
Up triangle: Entering chaos - start trend following
Down triangle: Entering stability - start mean reversion
Divergence Signals:
Bullish: Price makes low but Lyapunov rising (stability breaking down)
Bearish: Price makes high but Lyapunov falling (chaos dissipating)
Dashboard Information
Market State: Current regime (Chaotic/Stable/Transitioning)
Trading Bias: Specific strategy recommendation
Lyapunov λ: Raw value for precision
Signal Strength: Confidence in current regime
Last Change: Bars since last regime shift
Action: Clear trading directive
Trading Strategies
In Chaotic Regime (λ > threshold)
Follow trends aggressively: Breakouts have high success rate
Use momentum strategies: Moving average crossovers work well
Wider stops: Expect larger swings
Pyramid into winners: Trends tend to persist
In Stable Regime (λ < threshold)
Fade extremes: Mean reversion dominates
Use oscillators: RSI, Stochastic work well
Tighter stops: Smaller expected moves
Scale out at targets: Trends don't persist
In Transition Zone
Reduce position size: Uncertainty is high
Wait for confirmation: Let regime establish
Use options: Volatility strategies may work
Monitor closely: Quick changes possible
Advanced Techniques
- Multi-Timeframe Analysis
- Higher timeframe LMI for regime context
- Lower timeframe for entry timing
- Alignment = highest probability trades
- Divergence Trading
- Most powerful at regime boundaries
- Combine with support/resistance
- Use for early reversal detection
- Volatility Correlation
- Chaos often precedes volatility expansion
- Stability often precedes volatility contraction
- Use for options strategies
Originality & Innovation
LMI represents a genuine breakthrough in applying chaos theory to markets:
True Lyapunov Calculation: Not a simplified proxy but actual phase space reconstruction and divergence measurement
Rothko Aesthetic: Transforms complex math into meditative visual experience
Regime Detection: Identifies market state changes before price makes them obvious
Practical Application: Clear, actionable signals from theoretical physics
This is not a combination of existing indicators or a visual makeover of standard tools. It's a fundamental rethinking of how we measure and visualize market dynamics.
Best Practices
Start with defaults: Parameters are optimized for broad market conditions
Match to your timeframe: Adjust tau and evolution steps
Confirm with price action: LMI shows regime, not direction
Use appropriate strategies: Chaos = trend, Stability = reversion
Respect transitions: Reduce risk during regime changes
Alerts Available
Chaos Entry: Market entering chaotic regime - prepare for trends
Stability Entry: Market entering stable regime - prepare for ranges
Bullish Divergence: Potential bottom forming
Bearish Divergence: Potential top forming
Chart Information
Script Name: Lyapunov Market Instability (LMI) Recommended Use: All markets, all timeframes Best Performance: Liquid markets with clear regimes
Academic References
Takens, F. (1981). "Detecting strange attractors in turbulence"
Wolf, A. et al. (1985). "Determining Lyapunov exponents from a time series"
Rosenstein, M. et al. (1993). "A practical method for calculating largest Lyapunov exponents"
Note: After completing this indicator, I discovered @loxx's 2022 "Lyapunov Hodrick-Prescott Oscillator w/ DSL". While both explore Lyapunov exponents, they represent independent implementations with different methodologies and applications. This indicator uses phase space reconstruction for regime detection, while his combines Lyapunov concepts with HP filtering.
Disclaimer
This indicator is for research and educational purposes only. It does not constitute financial advice or provide direct buy/sell signals. Chaos theory reveals market character, not future prices. Always use proper risk management and combine with your own analysis. Past performance does not guarantee future results.
See markets through the lens of chaos. Trade the regime, not the noise.
Bringing theoretical physics to practical trading through the meditative aesthetics of Mark Rothko
Trade with insight. Trade with anticipation.
— Dskyz , for DAFE Trading Systems
Bitcoin as % Global M2 signalThis script provides signal system:
Buy signal: each time the YoY of the Global M2 rises more than 2.5% while the distance between the bitcoin price as a percentage of the Global M2 is below its yearly SMA.
Sell signal: the distance between the bitcoin price as a percentage of the Global M2 and its yearly SMA is > 0.7
This is a very simple system, but it seems to work pretty well to ride the bitcoin price cycle wave.
The parameters are hard coded but they can be easily changed to test different levels for both the buy and sell signals.
