mql5/Indicators/MyIndicators/Gaussian_Momentum_Pro.md

Gaussian Momentum Professional

1. Summary (Introduction)

The Gaussian Momentum Pro is an oscillator based on the concepts of John Ehlers. It applies a low-lag, 2-Pole Gaussian Filter to a momentum source (Close - Open) instead of the price.

While the standard Gaussian_Filter_Pro provides a smoothed representation of the trend, this indicator isolates and smooths the bar-by-bar momentum. The result is a responsive, zero-mean oscillator that measures the underlying strength and direction of price velocity.

The key advantage of using a Gaussian filter for this purpose is its ability to provide significant smoothing to the inherently noisy momentum data, while introducing minimal lag compared to traditional moving averages.

2. Mathematical Foundations and Calculation Logic

The indicator is a Gaussian-smoothed average of the Close - Open value of each bar.

Calculation Steps (Algorithm)

1. Calculate Momentum Source: For each bar, the source data is calculated as Momentum = Close - Open.
2. Apply Gaussian Filter: A 2-pole Gaussian filter is calculated on this Momentum data series. The recursive formula is: \text{Filt}_i = c_0 \times \text{Momentum}_i + a_1 \times \text{Filt}_{i-1} + a_2 \times \text{Filt}_{i-2} The c0, a1, a2 coefficients are derived from the user-selected Period.

3. MQL5 Implementation Details

• Unified Calculator (Gaussian_Filter_Calculator.mqh): This indicator uses the exact same, powerful calculator engine as the Gaussian_Filter_Pro. The only difference is that it is initialized in SOURCE_MOMENTUM mode.
• Heikin Ashi Integration: The indicator fully supports calculation on smoothed Heikin Ashi data (HA Close - HA Open).
• Stability via Full Recalculation: The indicator employs a full recalculation on every OnCalculate call to ensure the stateful, recursive calculation is always stable.

4. Parameters

• Period (InpPeriod): The cutoff period of the Gaussian filter, which controls its smoothing and responsiveness.
• Candle Source (InpCandleSource): Selects between Standard and Heikin Ashi candles for the Close - Open calculation.

5. Usage and Interpretation

The Gaussian Momentum is a classic zero-mean oscillator used for identifying momentum shifts and potential reversals. It is most powerful when used in conjunction with its companion smoother, the Gaussian_Filter_Pro.

Standalone Usage

• Zero-Line Crossover:
  • A cross above the zero line indicates that bullish momentum is taking control.
  • A cross below the zero line indicates that bearish momentum is dominant.
• Divergence:
  • Bullish Divergence: Price makes a new lower low, but the Gaussian Momentum makes a higher low. This signals weakening sell pressure.
  • Bearish Divergence: Price makes a new higher high, but the Gaussian Momentum makes a lower high. This signals weakening buy pressure.

Combined Strategy with Gaussian Filter (Primary Use)

The relationship between the momentum oscillator and its corresponding smoother provides a powerful timing signal.

• The Zero-Cross Predicts the Filter's Turning Point:
  • Buy Signal: When the Gaussian Momentum line crosses above the zero line, it signals that the Gaussian_Filter on the main chart is forming a trough (a bottom). This is a leading signal that the short-term downtrend is ending.
  • Sell Signal: When the Gaussian Momentum line crosses below the zero line, it signals that the Gaussian_Filter is forming a peak (a top). This is a leading signal that the short-term uptrend is ending.