mql5/Indicators/MyIndicators/ADX_Pro.md

Average Directional Index (ADX) Pro (v3.00)

Quantitative Trend Strength & Directional Movement Index (DMI) Suite

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1. Summary (Introduction)

ADX Pro is an institutional-grade implementation of J. Welles Wilder Jr.'s legendary Directional Movement System, comprising the Average Directional Index (ADX), Positive Directional Indicator (+DI), and Negative Directional Indicator (-DI).

Unlike momentum oscillators that oscillate with price swings, ADX measures the absolute strength and conviction of a market trend regardless of its direction. By quantifying the balance of power between buyers (+DI) and sellers (-DI), ADX Pro serves as the ultimate regime filter:

• Trend Absence / Consolidation Regime (ADX < 20.0): Market is in a low-conviction range; trend-following breakout systems should be paused, and mean-reversion strategies favored.
• Trend Confirmation Regime (ADX \ge 25.0): Validates that an authentic, directional momentum trend is in progress.
• Extreme Parabolic Climax (ADX \ge 40.0): Indicates an over-extended, mature trend vulnerable to momentum exhaustion or violent pullbacks.

┌────────────────────────────────────────────────────────────────────────┐
│                   THE DIRECTIONAL MOVEMENT SYSTEM                      │
├──────────────────────┬────────────────────────┬────────────────────────┤
│     Line Plot        │   Color Code           │   Core Role            │
├──────────────────────┼────────────────────────┼────────────────────────┤
│ ADX Line             │ clrDodgerBlue (Width:2)│ Absolute Trend Strength│
│ +DI Line             │ clrOliveDrab (Width:1) │ Positive Buying Power  │
│ -DI Line             │ clrTomato (Width:1)    │ Negative Selling Power │
└──────────────────────┴────────────────────────┴────────────────────────┘

Key Capabilities

• Definition-True Wilder Algorithm: Implements Wilder's exact recursive smoothing (RMA) across True Range, Directional Movement, and the DX series.
• Unified 2026 MTF Framework: Synchronized with DataSync_Tools.mqh to project higher-timeframe ADX and DMI curves (e.g., H1 or H4) onto lower-timeframe execution charts (M1, M5, M15) with flat, non-warping steps.
• Modular 3-Tier Architecture: Powered by DMI_Engine.mqh and ADX_Calculator.mqh with leak-free pointer safety.
• Synthetic Heikin Ashi Support: Computes smoothed directional vectors from synthetic Heikin Ashi candles to filter out false directional whipsaws.
• Dynamic Configurable Levels: Customizable horizontal thresholds for trend strength (25.0) and exhaustion (40.0).

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2. Mathematical Foundations & Directional Movement Mechanics

                 HIGH(t) - HIGH(t - 1)  ───►  +DM (Positive Directional Movement)
                 LOW(t - 1) - LOW(t)    ───►  -DM (Negative Directional Movement)
                                              │
                      ┌───────────────────────┴───────────────────────┐
                      │    Wilder's RMA Smoothing over Period P       │
                      └───────────────────────┬───────────────────────┘
                                              ▼
                    +DI = Smoothed(+DM) / Smoothed(TR) × 100
                    -DI = Smoothed(-DM) / Smoothed(TR) × 100
                                              │
                                              ▼
                    DX = | (+DI) - (-DI) | / [ (+DI) + (-DI) ] × 100
                                              │
                                              ▼
                      ADX = Wilder's RMA Smoothing on DX (Period P)

2.1. True Range (TR) Formulation

TR_t = \max\left( H_t, C_{t-1} \right) - \min\left( L_t, C_{t-1} \right)

2.2. Directional Movement Vectors (+DM, -DM)

\Delta H_t = H_t - H_{t-1}, \quad\quad \Delta L_t = L_{t-1} - L_t +DM_t = \begin{cases} \Delta H_t, & \text{if } \Delta H_t > \Delta L_t \text{ and } \Delta H_t > 0 \\ 0.0, & \text{otherwise} \end{cases} -DM_t = \begin{cases} \Delta L_t, & \text{if } \Delta L_t > \Delta H_t \text{ and } \Delta L_t > 0 \\ 0.0, & \text{otherwise} \end{cases}

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2.3. Wilder's Recursive Smoothing (RMA)

For any series X \in \{+DM, -DM, TR\}, the initial seed is the cumulative sum over lookback period P:

\text{Smoothed}(X)_P = \sum_{j=1}^{P} X_j

Subsequent bars update via Wilder's recursive smoothing equation:

\text{Smoothed}(X)_t = \text{Smoothed}(X)_{t-1} - \left( \frac{\text{Smoothed}(X)_{t-1}}{P} \right) + X_t = \frac{\text{Smoothed}(X)_{t-1} \cdot (P - 1) + X_t \cdot P}{P}

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2.4. Directional Indicators (+DI, -DI)

+DI_t = \left( \frac{\text{Smoothed}(+DM)_t}{\text{Smoothed}(TR)_t} \right) \times 100 -DI_t = \left( \frac{\text{Smoothed}(-DM)_t}{\text{Smoothed}(TR)_t} \right) \times 100

2.5. Directional Index (DX) & Average Directional Index (ADX)

DX_t = \begin{cases} \left( \frac{|+DI_t - -DI_t|}{+DI_t + -DI_t} \right) \times 100, & \text{if } (+DI_t + -DI_t) > 0 \\ 0.0, & \text{otherwise} \end{cases}

The final ADX curve begins at bar index t_{\text{seed}} = 2P - 1 as the arithmetic mean of the preceding P values of DX:

ADX_{2P-1} = \frac{1}{P} \sum_{j=0}^{P-1} DX_{2P-1-j}

Subsequent values update via Wilder's smoothing on DX:

ADX_t = \frac{ADX_{t-1} \cdot (P - 1) + DX_t}{P}

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3. MQL5 Architecture & Engineering Standards

┌────────────────────────────────────────────────────────┐
│                     DMI_Engine.mqh                     │
│    (Core Math: Computes Smoothed TR, +DM, -DM, ±DI)    │
└──────────────────────────┬─────────────────────────────┘
                           │ Feeds +DI & -DI Series
                           ▼
┌────────────────────────────────────────────────────────┐
│                   ADX_Calculator.mqh                   │
│    (DX Calculation & Wilder's Recursive ADX Engine)    │
└──────────────────────────┬─────────────────────────────┘
                           │ Outputs ADX, +DI, -DI in O(1)
                           ▼
┌────────────────────────────────────────────────────────┐
│                       ADX_Pro.mq5                      │
│    (Unified Wrapper: Native Timeframe & MTF Engine)    │
├──────────────────────────┬─────────────────────────────┤
│   Direct Mode (O(1))     │   Synchronized MTF Pipeline │
│   • Current Timeframe    │   • DataSync_Tools Daemon   │
│   • 3 Output Plots       │   • Staircase Flat-Force    │
└──────────────────────────┴─────────────────────────────┘

1. Modular 3-Tier Engine Hierarchy: Isolates low-level DMI physics (DMI_Engine.mqh) from high-level ADX smoothing (ADX_Calculator.mqh), allowing other oscillators in the suite to reuse DMI without recalculation overhead.
2. Leak-Free Pointer Protection: Factory methods (CreateEngine) explicitly verify pointer validity (CheckPointer) and safely free memory before re-allocation.
3. 2026 MTF Framework with Staircase Solution:
   • Asynchronous 1-second timer daemon (OnTimerUpdate) ensures higher-timeframe data synchronization without GUI freezes.
   • Dynamic staircase anchor (first_bar_of_forming_htf) synchronizes all lower-timeframe sub-bars belonging to the active higher-timeframe candle.

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4. Parameters Reference

Timeframe Settings

• InpTimeframe (default: PERIOD_CURRENT): Calculation timeframe. When set to PERIOD_CURRENT, it runs in native zero-lag mode. When set to a higher timeframe (e.g., PERIOD_H1, PERIOD_D1), it activates the synchronized MTF engine.

ADX Core Settings

• InpPeriodADX (default: 14): Wilder's lookback smoothing period (P) for DMI and ADX calculations.
• InpCandleSource (default: CANDLE_STANDARD): Candle price source (CANDLE_STANDARD or CANDLE_HEIKIN_ASHI).

Indicator Levels

• InpLevelTrend (default: 25.0): Key institutional trend strength threshold.
• InpLevelExtreme (default: 40.0): Strong trend / potential exhaustion boundary.
• InpLevelColor (default: clrSilver): Color of horizontal level lines.
• InpLevelStyle (default: STYLE_DOT): Line style of horizontal level lines.

Visual Settings

• InpColorADX (default: clrDodgerBlue): ADX trend strength line color (Width: 2, Solid).
• InpColorPDI (default: clrOliveDrab): +DI positive directional line color (Width: 1, Solid).
• InpColorNDI (default: clrTomato): -DI negative directional line color (Width: 1, Solid).

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5. Quantitative Trading Playbooks

┌────────────────────────────────────────────────────────────────────────┐
│                   ADX & DMI INSTITUTIONAL PLAYBOOKS                    │
├────────────────────────────────────────────────────────────────────────┤
│ 1. Regime Filter:        ADX < 20 = No Trend / Chop (Pause Breakouts) │
│                          ADX > 25 = Valid Directional Trend Active     │
│ 2. Directional Trigger:  +DI crosses above -DI while ADX > 25 = Buy    │
│                          -DI crosses above +DI while ADX > 25 = Sell   │
│ 3. Climax Exhaustion:    ADX > 40 turning downward = Scale Out Profits │
└────────────────────────────────────────────────────────────────────────┘

5.1. The ADX Regime Filter (Eliminating False Breakouts)

• Chop Rule (ADX < 20.0): When ADX is below 20.0, the market is range-bound. Disregard moving average crossovers and breakout signals. Favor mean-reversion boundary trades.
• Trend Confirmation (ADX \ge 25.0): A rising ADX crossing above 25.0 confirms that institutional trend expansion is active.

5.2. Directional Indicator Crossovers (+DI / -DI)

• Bullish Momentum Trigger: +DI crosses above -DI AND ADX > 25.0 (with ADX sloping upward) \rightarrow High-probability Long Trend Entry.
• Bearish Momentum Trigger: -DI crosses above +DI AND ADX > 25.0 (with ADX sloping upward) \rightarrow High-probability Short Trend Entry.

5.3. Multi-Timeframe Macro Trend Strength Filter

• Attach an H1-calculated ADX onto an M5 execution chart.
• Only take intraday long pullbacks on M5 when H1 ADX is above 25.0 AND H1 +DI is above H1 -DI. This ensures you are trading strictly aligned with higher-timeframe institutional trend momentum.

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6. Indicator Buffer Map (For Developers & EA Integration)

Buffer Index	Name	Type	Description
0	BufferADX	INDICATOR_DATA	Average Directional Index (Main Trend Strength)
1	BufferPDI	INDICATOR_DATA	Positive Directional Indicator (+DI)
2	BufferNDI	INDICATOR_DATA	Negative Directional Indicator (-DI)

All buffers strictly maintain non-series chronological order (ArraySetAsSeries = false), ensuring instant compatibility with Expert Advisors and scanner dashboards via iCustom().