diff --git a/Indicators/MyIndicators/Authors/Ehlers/1_Smoothers/Windowed_MA_Pro.md b/Indicators/MyIndicators/Authors/Ehlers/1_Smoothers/Windowed_MA_Pro.md index c12808d..5df4cf3 100644 --- a/Indicators/MyIndicators/Authors/Ehlers/1_Smoothers/Windowed_MA_Pro.md +++ b/Indicators/MyIndicators/Authors/Ehlers/1_Smoothers/Windowed_MA_Pro.md @@ -2,43 +2,39 @@ ## 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. +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 a **Hann Window** function 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. +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 applies a mathematically superior cosine-based weighting scheme (Hann Window) 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. +The indicator is a weighted moving average, where the weights are determined by the Hann window 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: $W_j = 0.5 \times (1 - \cos(\frac{2\pi \times j}{N-1}))$ +1. **Calculate Weights:** For each position `j` within the `N`-period window, a specific 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. +* **Unified Calculator (`Windowed_MA_Calculator.mqh`):** The calculation is handled by a dedicated calculator class. +* **Optimized Incremental Calculation (O(1)):** + Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm. + * **State Tracking:** It utilizes `prev_calculated` to process only new bars. + * **Persistent Buffers:** The internal price buffer persists its state between ticks. + * **Pre-calculated Weights:** The Hann weights are calculated only once during initialization, making the runtime calculation extremely fast. * **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. +* **Period (`InpPeriod`):** The lookback period (`N`) for the moving average. (Default: `20`). +* **Applied Price (`InpSourcePrice`):** The source price for the calculation. (Standard or Heikin Ashi). ## 5. Usage and Interpretation @@ -46,7 +42,6 @@ The Windowed MA should be used as a high-quality replacement for a standard Simp * **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)**