Average Directional Index (ADX) Pro

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.

Our ADX_Pro implementation is a unified, professional version that allows the calculation to be based on either standard or Heikin Ashi candles.

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)

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})]
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)
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}
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}
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 follows a modern, object-oriented design pattern to ensure stability, reusability, and maintainability. The logic is separated into a main indicator file, a dedicated calculator engine, and a shared core engine.

Shared Core Engine (DMI_Engine.mqh): The fundamental calculation of Directional Movement (+DI, -DI) is outsourced to a shared engine. This ensures that both the ADX and the DMI Stochastic indicators use the exact same, validated mathematical core, eliminating code duplication and potential inconsistencies.
Modular Calculator Engine (ADX_Calculator.mqh): The ADX-specific logic (calculating the DX and smoothing it to get the ADX) is encapsulated here. This calculator orchestrates the DMI_Engine to get the raw data and then performs the final steps.
Object-Oriented Design (Composition & Inheritance):
- The CADXCalculator uses Composition to include the CDMIEngine.
- The Heikin Ashi support is implemented via a Factory Pattern in the CADXCalculator_HA subclass, which instantiates a specialized CDMIEngine_HA. This keeps the main logic clean and agnostic of the data source.
Optimized Incremental Calculation: Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm.
- It utilizes the prev_calculated state to determine the exact starting point for updates.
- The internal buffers persist their state between ticks, allowing the recursive Wilder's Smoothing algorithm to continue seamlessly from the last known value.
- This results in O(1) complexity per tick, ensuring instant updates and zero lag.

4. Parameters (`ADX_Pro.mq5`)

ADX Period (InpPeriodADX): The lookback period used for all internal calculations. Wilder's original recommendation and the most common value is 14.
Candle Source (InpCandleSource): Allows the user to select the candle type for the initial calculation of directional movement.
- CANDLE_STANDARD: Uses the standard chart's OHLC data.
- CANDLE_HEIKIN_ASHI: Uses smoothed Heikin Ashi data.

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.

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