mql5/Indicators/MyIndicators/ADX.md

Average Directional Index (ADX)

1. Summary (Introduction)

The Average Directional Index (ADX), developed by J. Welles Wilder, is a widely used technical indicator designed to measure the strength of a trend, regardless of its direction. It does not indicate whether the trend is bullish or bearish, but only quantifies its momentum.

The ADX system consists of three lines:

• ADX Line: The main line that indicates trend strength.
• +DI (Positive Directional Indicator): A line that measures the strength of the upward price movement.
• -DI (Negative Directional Indicator): A line that measures the strength of the downward price movement.

It is a powerful tool for traders to distinguish between trending and non-trending (ranging) market conditions.

2. Mathematical Foundations and Calculation Logic

The ADX calculation is a complex, multi-stage process that relies heavily on Wilder's smoothing technique (a specific type of Smoothed or Running Moving Average - SMMA/RMA).

Required Components

• ADX Period (N): The lookback period for all calculations (e.g., 14).
• Directional Movement (+DM, -DM): Measures the portion of the current bar's range that is outside the previous bar's range.
• True Range (TR): The standard measure of a single bar's volatility.

Calculation Steps (Algorithm)

1. Calculate Directional Movement and True Range: For each period, calculate:

   • \text{Up Move} = \text{High}_i - \text{High}_{i-1}
   • \text{Down Move} = \text{Low}_{i-1} - \text{Low}_i
   • If \text{Up Move} > \text{Down Move} and \text{Up Move} > 0, then \text{+DM} = \text{Up Move}, else \text{+DM} = 0.
   • If \text{Down Move} > \text{Up Move} and \text{Down Move} > 0, then \text{-DM} = \text{Down Move}, else \text{-DM} = 0.
   • \text{True Range (TR)} = \text{Max}[(\text{High}_i - \text{Low}_i), \text{Abs}(\text{High}_i - \text{Close}_{i-1}), \text{Abs}(\text{Low}_i - \text{Close}_{i-1})]

2. Smooth +DM, -DM, and TR: Apply Wilder's smoothing method over the period N.

   • Initialization: The first value is the sum of the first N periods. \text{Smoothed +DM}_{N} = \sum_{i=1}^{N} \text{+DM}_i
   • Recursive Calculation: \text{Smoothed +DM}_i = \text{Smoothed +DM}_{i-1} - \frac{\text{Smoothed +DM}_{i-1}}{N} + \text{+DM}_i
   • (The same logic applies to -DM and TR)

3. Calculate Directional Indicators (+DI, -DI): \text{+DI}_i = 100 \times \frac{\text{Smoothed +DM}_i}{\text{Smoothed TR}_i} \text{-DI}_i = 100 \times \frac{\text{Smoothed -DM}_i}{\text{Smoothed TR}_i}

4. Calculate the Directional Index (DX): \text{DX}_i = 100 \times \frac{\text{Abs}(\text{+DI}_i - \text{-DI}_i)}{\text{+DI}_i + \text{-DI}_i}

5. Calculate the Final ADX: The ADX is a Wilder-smoothed moving average of the DX.

   • Initialization: The first ADX value is a simple average of the first N DX values.
   • Recursive Calculation: \text{ADX}_i = \frac{(\text{ADX}_{i-1} \times (N-1)) + \text{DX}_i}{N}

3. MQL5 Implementation Details

Our MQL5 implementation was refactored to be highly robust, clear, and consistent with our established "Wilder Algorithm".

• Stability via Full Recalculation: We employ a "brute-force" full recalculation within the OnCalculate function. For a complex, multi-stage indicator like the ADX, this is the most reliable method to prevent calculation errors.

• Consensus Wilder Algorithm: The implementation strictly follows our established two-step algorithm for Wilder's smoothing:

  1. Robust Initialization: The first smoothed value is calculated non-recursively (as a simple sum for +DM, -DM, TR, and as a simple average for ADX).
  2. Efficient Recursive Calculation: All subsequent values are calculated using the efficient formula: Previous Value - (Previous Value / N) + Current Value.

• Clear, Staged Calculation: The OnCalculate function is structured into clear, sequential steps, each handled by a dedicated for loop. This improves code readability and makes the complex logic easy to follow:

  1. Step 1: Raw +DM, -DM, and TR values are calculated and stored in temporary arrays.
  2. Step 2: The raw values are smoothed using our Wilder algorithm.
  3. Step 3: The +DI, -DI, and DX values are calculated from the smoothed data.
  4. Step 4: The final ADX line is calculated by applying the Wilder algorithm to the DX values.

• Heikin Ashi Variant (ADX_HeikinAshi.mq5):

  • Our toolkit also includes a Heikin Ashi version of this indicator. The calculation logic is identical, but it uses the smoothed Heikin Ashi ha_high, ha_low, and ha_close values as its input.
  • This results in a smoother ADX system that reflects the momentum of the underlying Heikin Ashi trend, effectively filtering out some of the market noise that can cause the +DI and -DI lines to cross frequently.

4. Parameters

• ADX Period (InpPeriodADX): The lookback period used for all internal calculations (+DM, -DM, TR, and the final ADX smoothing). Wilder's original recommendation and the most common value is 14.

5. Usage and Interpretation

• Trend Strength: The primary signal is the ADX line itself.
  • ADX < 25: Weak or non-existent trend (ranging market). Trend-following strategies should be avoided.
  • ADX > 25: Strong trend. The higher the ADX, the stronger the trend.
  • Rising ADX: The trend is gaining strength.
  • Falling ADX: The trend is losing strength.
• Trend Direction (+DI and -DI Crossover):
  • When the +DI line (green) crosses above the -DI line (red), it suggests the start of a bullish trend.
  • When the -DI line (red) crosses above the +DI line (green), it suggests the start of a bearish trend.
• Trade Confirmation: A common strategy is to wait for a +DI/-DI crossover and then confirm that the ADX line is above 25 (or rising) before entering a trade. This helps to filter out signals that occur in weak or non-trending markets.