STD-Filtered, Gaussian Moving Average (GMA)

The STD-Filtered, Gaussian Moving Average (GMA) indicator implements a 1-4 pole Gaussian filter optimized with standard deviation noise reduction to provide smooth, low-lag trend identification. This tool functions similarly to the Fisher Transform, aiming to isolate significant price movements while rejecting high-frequency noise.

Usage

The Usage section describes how the script can be used to identify trend direction and potential reversals. Users can observe the color-coded Gaussian Moving Average (GMA) line on the chart: a green line indicates an upward trend, while a red line indicates a downward trend.

The primary settings allow for granular control over how the filter reacts to price volatility. By adjusting the "Filter Deviations" and "Filter Options," traders can decide whether to apply noise filtering to the raw price source, the calculated GMA, or both. For example, setting the filter to 1 standard deviation will ignore price changes that fall within that range, effectively stalling the indicator until a significant move occurs.

The script also includes built-in signals:

• Long (L): Triggered when the GMA crosses above its previous value after a bearish period.
• Short (S): Triggered when the GMA crosses below its previous value after a bullish period.

Details

The Gaussian filter, originally described by John F. Ehlers in "Rocket Science For Traders," is a low-pass filter designed to reduce lag compared to traditional moving averages. Its transfer response follows a Gaussian bell-shaped curve.

A unique aspect of this implementation is the "Poles" setting. In a Gaussian filter:

• 1 Pole: Functionally equivalent to an Exponential Moving Average (EMA).
• 2 Poles: Equivalent to a double EMA (EMA of an EMA).
• 3 Poles: Equivalent to a triple EMA.
• 4 Poles: Provides even sharper high-frequency rejection.

The standard deviation filter included in this script helps prevent "whipsaws" in sideways markets. It evaluates the difference between the current value and the previous value; if the difference is less than the specified standard deviation threshold, the value is held constant.

Settings

Source Settings

• Heiken-Ashi Better Smoothing: Selects the smoothing algorithm (AMA, T3, or Kaufman) for HA-based sources.
• Source: Provides various price source options, including standard OHLC, Median, Heikin-Ashi variants, and "Better" smoothed variants.

Basic Settings

• Period: The lookback period for the Gaussian filter.
• Poles: The number of poles (1 to 4) used in the filter calculation. Higher poles increase smoothing and frequency rejection.

Filter Settings

• Filter Options: Determines where the standard deviation filter is applied (Price, GMA, Both, or None).
• Filter Deviations: The number of standard deviations used for the noise filter threshold.
• Filter Period: The lookback period used to calculate the standard deviation for the filter.

UI Options

• Color bars?: Toggles price bar coloring based on the current trend.
• Show signals?: Enables or disables the visual Long/Short labels on the chart.

Moving Average Inputs

• Kaufman's Adaptive MA (KAMA) Only: Adjusts the Fast and Slow end constants for KAMA-based sources.
• Adaptive Moving Average (AMA) Only: Adjusts the Fast and Slow periods for AMA-based sources.

FAQ

How do the different "Poles" affect the indicator?
Increasing the number of poles results in a steeper roll-off of high-frequency noise. While more poles typically add a small amount of lag, a Gaussian filter with multiple poles still maintains significantly less lag than a Butterworth filter of the same degree.

What does the "Filter Deviations" setting do?
It acts as a volatility gate. If the price (or GMA) moves less than the specified standard deviations within the filter period, the indicator remains flat. This is useful for avoiding false signals in consolidating markets.

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