mql5/Indicators/MyIndicators/DMH_Pro.md

DMH Professional (Directional Movement with Hann Windowing)

1. Summary (Introduction)

The DMH (Directional Movement with Hann Windowing) is John Ehlers' modern re-interpretation of J. Welles Wilder's classic Directional Movement concept. Ehlers' goal was to "freshen up" the original DMI/ADX system for modern algorithmic trading by removing what he considered redundant components and improving the filtering method.

Instead of the traditional three-line ADX system (+DI, -DI, ADX), the DMH produces a single, smooth oscillator that fluctuates around a zero line. This line directly represents the balance between bullish (PlusDM) and bearish (MinusDM) pressure.

• When the DMH is above zero, upward directional movement is dominant.
• When the DMH is below zero, downward directional movement is dominant.

The indicator uses a sophisticated two-stage smoothing process, combining an EMA with a Hann-windowed FIR filter to create a much cleaner, lower-noise signal than the classic +DI/-DI lines.

2. Mathematical Foundations and Calculation Logic

The DMH indicator transforms the raw Directional Movement values into a single, heavily smoothed oscillator.

Required Components

• Period (N): The lookback period for both smoothing stages.
• Source Price: The High and Low of each bar.

Calculation Steps (Algorithm)

1. Calculate Raw Directional Movement (DM): For each bar, calculate the classic PlusDM and MinusDM values based on the change in highs and lows relative to the previous bar.
2. Calculate DM Difference: Instead of normalizing with ATR, Ehlers immediately takes the difference: \text{DM Diff}_i = \text{PlusDM}_i - \text{MinusDM}_i
3. First Smoothing (EMA): The raw DM Diff series is smoothed with an Exponential Moving Average (EMA) of period N.
4. Second Smoothing (Hann FIR Filter): The resulting EMA series is then smoothed again using a Hann-windowed Finite Impulse Response (FIR) filter of period N. This is a weighted moving average where the weights are derived from a cosine function (the Hann window), which provides superior smoothing compared to a simple average.
5. Final Output: The result of this second smoothing is the final DMH line.

3. MQL5 Implementation Details

• Self-Contained Calculator (DMH_Calculator.mqh): The entire multi-stage calculation is encapsulated within a dedicated, reusable calculator class.
• Heikin Ashi Integration: An inherited _HA class allows the initial PlusDM and MinusDM calculation to be performed seamlessly on smoothed Heikin Ashi data.
• Two-Stage Smoothing: The calculator accurately implements the two distinct smoothing phases: a recursive EMA followed by a non-recursive, weighted FIR filter.
• Stability via Full Recalculation: The indicator employs a full recalculation on every OnCalculate call to ensure the stateful EMA calculation and the FIR filter are always perfectly synchronized and stable.

4. Parameters

• Period (InpPeriod): The lookback period (N) used for both the initial EMA and the final Hann FIR filter. The default, as in Wilder's original work, is 14.
  • A shorter period will result in a faster, more volatile oscillator.
  • A longer period will result in a smoother, slower oscillator that only reflects major momentum shifts.
• Source (InpSource): Selects between Standard and Heikin Ashi candles for the initial DM calculation.

5. Usage and Interpretation

The DMH is a momentum oscillator used to identify the dominant directional pressure and its turning points. Ehlers suggests two ways to interpret its signals.

1. Zero-Line Crossover (Trend Direction)

This is the most basic signal, similar in concept to a +DI/-DI crossover.

• Buy Signal / Bullish Bias: The DMH line crosses above the zero line. This indicates that bullish pressure is now stronger than bearish pressure.
• Sell Signal / Bearish Bias: The DMH line crosses below the zero line. This indicates that bearish pressure has taken control.
• Note: Ehlers points out that these signals have a natural lag and are better used for confirmation rather than primary entry triggers.

2. Peaks and Valleys (Timing Reversals - Ehlers' Preferred Method)

This method uses the turning points of the smooth DMH line to anticipate reversals in momentum.

• Buy Signal (Valley): A trough or valley in the DMH line (especially below the zero line) indicates that bearish momentum has reached its peak and is exhausting. A turn upwards from a valley is a potential buy signal.
• Sell Signal (Peak): A peak or crest in the DMH line (especially above the zero line) indicates that bullish momentum is exhausting. A turn downwards from a peak is a potential sell signal.

Important Consideration: Use with a Trend Filter

Like most oscillators, the DMH is most effective when its signals are filtered by the primary trend.

• Uptrend Rule: In a clear uptrend (e.g., price is above a 200-period EMA), focus on Buy signals (valleys in the DMH) as potential entry points during pullbacks.
• Downtrend Rule: In a clear downtrend, focus on Sell signals (peaks in the DMH) as potential entry points during corrective rallies.