STD-Filtered, Gaussian-Kernel-Weighted Moving Average

The STD-Filtered, Gaussian-Kernel-Weighted Moving Average indicator provides a non-parametric regression-based smoothing tool that utilizes a Gaussian kernel function and standard deviation filtering to minimize price noise while maintaining trend responsiveness.

Usage

The Usage section describes how the script can be used, particularly in identifying trends and potential reversal points through smoothed price action.

• Trend Identification: The indicator colors the moving average line and price bars based on the current trend. A green line indicates a bullish trend, while a red line indicates a bearish trend.
• Signal Generation: The tool provides "L" (Long) and "S" (Short) labels when the Gaussian-weighted output crosses its previous value. Users should ensure the current bar closes before acting on a signal to avoid issues with intraday fluctuations.
• Source Selection: The indicator supports a wide range of source types, including standard price inputs, Heikin-Ashi variations, and smoothed "Better Heikin-Ashi" (HAB) inputs.
• Filter Application: Users can choose to apply a standard deviation filter to the raw price source, the final output signal, or both. This helps in "stepping" the moving average, keeping the value static until price movement exceeds a specific volatility threshold.

Details

The Gaussian-Kernel-Weighted Moving Average (GKWMA) is built on the concept of Kernel estimation. Unlike standard regression models that may repaint by predicting past values based on future data, this implementation calculates the weighted function at each bar to predict the current value, making it suitable for real-time trading.

The Gaussian kernel function is defined as: K(u) = (1 / sqrt(2pi)) * e^(-0.5 * (j / bw)^2)

Where:

• j represents the distance from the current point.
• bw (Bandwidth) acts as the smoothing parameter. A higher bandwidth increases the smoothing effect but may introduce more lag.

The indicator also incorporates a volatility-based filter. It calculates the standard deviation over a user-defined period and only updates the price or signal value if the change from the previous bar exceeds the product of the standard deviation and the "Filter Deviations" multiplier.

Settings

Source Settings

• Heiken-Ashi Better Smoothing: Selects the smoothing method (AMA, T3, or Kaufman) for HAB source types.
• Source: Determines the input price data, ranging from standard Close to complex Trend Biased and Heikin-Ashi derivatives.

Gaussian-Kernel Settings

• Bandwidth: Controls the width of the Gaussian distribution. Higher values result in a smoother, slower-moving average.

Filter Settings

• Filter Options: Choose whether to apply the standard deviation filter to the input "Price", the "GKS Filter" (output), or "Both".
• Filter Deviations: The multiplier for the standard deviation. Higher values create a more "stepped" or stagnant line that only moves during significant volatility.
• Filter Period: The lookback period used to calculate the standard deviation for the filter.

UI Options

• Color bars?: Enables or disables the coloring of price bars based on trend direction.
• Show signals?: Toggles the visibility of the Long and Short plot shapes.

Moving Average Inputs

• Kaufman's / AMA Settings: These parameters control the internal calculations if Kaufman or Adaptive Moving Average smoothing is selected in the Source Settings.

FAQ

How do I adjust the lag of the moving average? The lag is primarily controlled by the Bandwidth setting. Lowering the bandwidth makes the indicator more responsive to recent price changes, while increasing it provides a smoother, more lagged trend line.

What does the Standard Deviation filter do? The filter prevents the moving average from changing value unless the price move is significant relative to recent volatility. This is useful for avoiding "whipsaws" during sideways or low-volatility markets.

How can I access this indicator? You can get access on the LuxAlgo Library for charting platforms like TradingView, MetaTrader (MT4/MT5), and NinjaTrader for free.