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Fourier Adjusted Volume Zone Oscillator [BackQuant]

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Fourier Adjusted Volume Zone Oscillator [BackQuant]
Welcome to BackQuant's FSVZO, Primarily we decided to combine the Fourier analysis to a leading indicator concept. Since in concept it can be beneficial.
We also decided to add in the momentum velocity indicator as a point of confluence.
Which will be discussed later in how it can be used in a trading system. For now onto the boring stuff, please read all of this and enjoy!

Fourier ? What and Why:
Fourier transforms are a mathematical technique used for transforming signals between time and frequency domains. In the context of financial markets, this allows analysts to deconstruct price movements into constituent sinusoidal waves. By isolating these waves, traders can identify the dominant market cycles and trends hidden within the 'noise' of short-term price fluctuations.

Empirical Evidence and Benefits:
Cycle Identification: Empirical studies have shown that markets exhibit cyclical behaviors due to various economic, geopolitical, and psychological factors. Fourier filtering helps in pinpointing these cycles, even in seemingly random market movements.
Trend Detection: By highlighting dominant frequencies, traders can more accurately determine the prevailing trend direction, aiding in trend-following or contrarian strategies.
Volatility Clarity: Filtering out noise enhances the visibility of true market volatility, crucial for risk management and strategy adjustment.

Why the Volume Zone Oscillator (VZO) and Origins + Advantages:
The VZO was developed by Walid Khalil and David Steckler and introduced in the "Stocks & Commodities" magazine in 2009. It integrates volume with price movements to gauge the flow of buying and selling pressure. Unlike traditional volume indicators that solely quantify trading volume, the VZO interprets volume's impact on price direction, offering insights into the strength or weakness of a price trend.

Empirical Evidence and Benefits:
Market Sentiment: Volume is a key indicator of market sentiment. High volume accompanying price movements indicates strong sentiment, whereas low volume suggests a lack of conviction. The VZO makes this analysis quantifiable.
Overbought/Oversold Conditions: By quantifying where the current volume-weighted price is within its range, the VZO helps identify potential reversals, providing actionable signals for entering or exiting trades.
Trend Confirmation: The VZO's ability to confirm price trends with volume adds an extra layer of validation to trading signals, reducing the likelihood of false breakouts or breakdowns.

Why we Decided to Combine Them
The integration of Fourier filtering with the VZO offers a comprehensive view of the market by combining the geometric clarity of price movements with the psychological insights provided by volume analysis. This synergy allows for a more nuanced understanding of market dynamics.

Enhanced Signal Accuracy: The combination reduces the chances of false signals. Fourier filtering's trend and cycle identification, combined with the VZO's volume-based confirmation, can significantly enhance trading decision accuracy.

Market Turns and Continuations: Fourier analysis can indicate potential turning points or continuation patterns, which, when confirmed with volume analysis through the VZO, provides a robust signal for traders to act upon.
Adaptability: Both tools adapt well to various market conditions, making this combination versatile across different trading instruments and timeframes.

Empirical Evidence:
While specific empirical studies directly analyzing the combined effectiveness of Fourier filtering and VZO might be scarce, the foundational research supporting each method individually provides strong evidence of their validity. Academic and practical applications in financial markets have demonstrated the value of both Fourier analysis for cycle detection and volume-based oscillators like the VZO for assessing market strength and sentiment. Together, they offer a compelling toolkit for traders aiming to refine their market analysis and strategy execution.

USER INPUTS
Momentum Velocity Group
Show Confluence Momentum Velocity?: This toggle allows users to decide whether they want to display the momentum velocity indicator on their chart. It's designed to show the momentum of price movements, potentially indicating acceleration or deceleration in price trends.
Calculation Source: This setting lets users select the price data used for calculating the momentum velocity. Common options include the close, open, high, low, or an average of these prices. The choice depends on what aspect of price action the trader wishes to analyze.
Lookback Period: Determines the number of bars used to calculate the momentum. A longer period may smooth out the indicator, reducing sensitivity to recent price changes, while a shorter period may make the indicator more responsive to new information.
Use Adaptive Filtering?: Enables the use of adaptive filtering for the momentum calculation. This feature adjusts the indicator's sensitivity based on recent market volatility, potentially improving the indicator's responsiveness to market changes.
Adaptive Lookback Period: Specifies the period for the adaptive filter. This setting fine-tunes how rapidly the filter adjusts to changes in market conditions.

FSVZO Group
Show FSVZO?: This input controls whether the Fourier Smoothed Volume Zone Oscillator is displayed on the chart. It's the main feature of the script, combining Fourier analysis with volume data to provide insights into market dynamics.
Calculation Source for FSVZO: Similar to the momentum velocity calculation source, this setting allows users to choose the price data (close, open, high, low, or an average) that will be used for FSVZO calculations.
Calculation Period: Defines the length of the window for Fourier analysis and VZO calculation. This period can affect the sensitivity and smoothing of the indicator.
Show FSVZO Band Filler? (Ribbon): When enabled, this feature displays a filled area or ribbon on the chart, making it easier to visualize the oscillator's movement and trends.
Show FSVZO Moving Average (Ema)?: This toggle allows the display of an Exponential Moving Average (EMA) of the FSVZO, which can help smooth out its movements and provide a clearer trend direction.
MA Period: Specifies the length of the moving average applied to the FSVZO. Adjusting this period can affect the smoothness and lag of the trend indication.
Smooth VZO (Reduces noise, but increases its accuracy): Enables smoothing of the Volume Zone Oscillator to reduce noise and potentially increase the accuracy of its signals.
Smooth Period: Defines the smoothing period for the VZO, affecting how much noise reduction is applied.

UI Settings Group
Show Static Overbought and Oversold Levels?: Enables the display of predetermined levels that indicate overbought or oversold conditions, helping traders identify potential reversal points.
Show Adaptive Levels?: Allows the use of dynamic, market-condition-adjusted levels for overbought and oversold indicators, offering a more nuanced view of market extremes.
Show Detected Trend Shifts?: This setting controls the display of markers or indications when the script detects potential shifts in market trends, based on the oscillator's movements.
Trendshift Shader?: When enabled, this feature visually highlights areas on the chart where trend shifts are detected, improving the visibility of these important signals.

DIVERGENCES Group
Show Detected Divergences?: This option toggles the display of divergences between price action and the oscillator, which can signal potential reversals.
Use extra filtering when detecting divergences?: Enables additional criteria for identifying divergences, potentially improving the reliability of these signals.
Paint bars when Divergences are detected?: This feature changes the color of price bars when divergences are identified, making them stand out on the chart.
How to calculate divergences: Allows users to choose the method for calculating divergences, affecting the sensitivity and types of divergences that are identified.
Only calculate divergences on values absolutely greater than this: Sets a threshold for divergence calculation, focusing on more significant divergences and reducing noise.

Each input is designed to offer flexibility and control to the user, enabling a highly customizable experience tailored to individual trading strategies and market conditions.

How Can it Be Used in a Trading System
There are a few key ways it can be used, the main way is going to be the trend of the band/ ribbon. As that denotes the primary trend. Thus, if it were to trend up and reach the static overbought zone, there is a high probability of a reversion. This will also work well when it is in an extreme zone and there is a divergence.

Other ways of using it, it taking profit when there is an extreme background hue. Or potentially starting to get ready to buy on a higher timeframe if there is a extreme oversold background hue.

For more clear trends out of the FSVZO you may choose to use the moving average crossing the midline in confluence with the momentum velocity.

Please use with caution, nothing BackQuant or associated entities do are financial advice. please do not use this or any other indicator alone, they are not meant to be used in isolation.

Thus following all of the key points here are some sample backtests on the 1D Chart
Disclaimer: Backtests are based off past results, and are not indicative of the future.
This is using the Midline Crossover of the FSVZO: