mql5/Indicators/MyIndicators/Windowed_MA_Pro.md

Windowed MA Professional

1. Summary (Introduction)

The Windowed MA Pro is an indicator based on John Ehlers' research into advanced Finite Impulse Response (FIR) filters. It serves as a superior alternative to the Simple Moving Average (SMA) by employing "windowing" functions to create a smoother, more responsive output.

A standard SMA uses a "rectangular window," giving equal weight to all prices in the lookback period, which results in poor filtering characteristics. This indicator allows the user to apply mathematically superior weighting schemes:

1. Triangular Window: A simple weighting that gives the most emphasis to the middle of the lookback period.
2. Hann Window: A more advanced, cosine-based weighting function that provides excellent smoothing and is Ehlers' recommended choice for most trading applications.

The result is a high-fidelity moving average that produces a cleaner representation of the trend with less noise than a standard SMA.

2. Mathematical Foundations and Calculation Logic

The indicator is a weighted moving average, where the weights are determined by the selected windowing function.

Calculation Steps (Algorithm)

For each bar, the indicator looks back over the last N periods.

1. Calculate Weights: For each position j within the N-period window, a specific weight is calculated based on the chosen Window Type.
   • SMA: Weight = 1
   • Triangular: The weight increases linearly to the midpoint of the window and then decreases.
   • Hann: The weight is calculated using a cosine formula, creating a smooth, bell-shaped curve: W_j = 0.5 \times (1 - \cos(\frac{2\pi \times j}{N-1}))
2. Calculate Weighted Sum: The source price at each position is multiplied by its corresponding weight and summed up.
3. Normalize: The final indicator value is the weighted sum divided by the sum of all weights.

3. MQL5 Implementation Details

• Unified Calculator (Windowed_MA_Calculator.mqh): The calculation for all window types is handled by a single, flexible calculator class. The user's choice determines which weighting formula is used inside the calculation loop.
• Heikin Ashi Integration: The indicator fully supports calculation on smoothed Heikin Ashi data.
• FIR-based Logic: This is a non-recursive (FIR) filter. Its calculation at any given bar depends only on the last N prices.
• Stability via Full Recalculation: The indicator employs a full recalculation on every OnCalculate call.

4. Parameters

• Window Type (InpWindowType): Allows the user to select the weighting function: SMA, Triangular, or Hann. Hann is recommended for the best smoothing.
• Period (InpPeriod): The lookback period (N) for the moving average.
• Applied Price (InpSourcePrice): The source price for the calculation (e.g., Close, Open, etc.).
• Candle Source (InpCandleSource): Selects between Standard and Heikin Ashi candles.

5. Usage and Interpretation

The Windowed MA should be used as a high-quality replacement for a standard Simple Moving Average.

• Trend Identification: Use it to identify the direction of the trend. Price trading above the line indicates an uptrend; price below indicates a downtrend.
• Dynamic Support and Resistance: The line acts as a dynamic S/R level. Due to its superior smoothing, it often provides more reliable support/resistance than a standard SMA.
• Crossover Systems: A two-line crossover system using a fast and a slow Windowed MA (especially with the Hann window) will produce smoother and potentially cleaner signals than a standard SMA crossover system.

Combined Strategy with Windowed Momentum (Advanced)

The true power of the Ehlers windowing concept is revealed when using the Windowed_MA_Pro and Windowed_Momentum_Pro indicators together. A key relationship exists between them:

• The Momentum Oscillator's zero-cross predicts the Moving Average's turning point.
  • When the Windowed_Momentum oscillator crosses above its zero line, it signals that the Windowed_MA is forming a trough (a bottom).
  • When the Windowed_Momentum oscillator crosses below its zero line, it signals that the Windowed_MA is forming a peak (a top).

This relationship can be used to anticipate changes in the short-term trend defined by the moving average, providing a powerful leading signal.