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# Average Directional Index (ADX) Pro (v3.00)
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Quantitative Trend Strength & Directional Movement Index (DMI) Suite
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---
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## 1. Summary (Introduction)
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**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)**.
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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:
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* **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.
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* **Trend Confirmation Regime ($ADX \ge 25.0$):** Validates that an authentic, directional momentum trend is in progress.
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* **Extreme Parabolic Climax ($ADX \ge 40.0$):** Indicates an over-extended, mature trend vulnerable to momentum exhaustion or violent pullbacks.
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ THE DIRECTIONAL MOVEMENT SYSTEM │
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├──────────────────────┬────────────────────────┬────────────────────────┤
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│ Line Plot │ Color Code │ Core Role │
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├──────────────────────┼────────────────────────┼────────────────────────┤
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│ ADX Line │ clrDodgerBlue (Width:2)│ Absolute Trend Strength│
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│ +DI Line │ clrOliveDrab (Width:1) │ Positive Buying Power │
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│ -DI Line │ clrTomato (Width:1) │ Negative Selling Power │
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└──────────────────────┴────────────────────────┴────────────────────────┘
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```
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### Key Capabilities
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* **Definition-True Wilder Algorithm:** Implements Wilder's exact recursive smoothing (RMA) across True Range, Directional Movement, and the DX series.
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* **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.
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* **Modular 3-Tier Architecture:** Powered by `DMI_Engine.mqh` and `ADX_Calculator.mqh` with leak-free pointer safety.
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* **Synthetic Heikin Ashi Support:** Computes smoothed directional vectors from synthetic Heikin Ashi candles to filter out false directional whipsaws.
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* **Dynamic Configurable Levels:** Customizable horizontal thresholds for trend strength ($25.0$) and exhaustion ($40.0$).
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---
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## 2. Mathematical Foundations & Directional Movement Mechanics
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```text
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HIGH(t) - HIGH(t - 1) ───► +DM (Positive Directional Movement)
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LOW(t - 1) - LOW(t) ───► -DM (Negative Directional Movement)
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│
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┌───────────────────────┴───────────────────────┐
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│ Wilder's RMA Smoothing over Period P │
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└───────────────────────┬───────────────────────┘
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▼
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+DI = Smoothed(+DM) / Smoothed(TR) × 100
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-DI = Smoothed(-DM) / Smoothed(TR) × 100
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│
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▼
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DX = | (+DI) - (-DI) | / [ (+DI) + (-DI) ] × 100
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│
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▼
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ADX = Wilder's RMA Smoothing on DX (Period P)
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```
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### 2.1. True Range ($TR$) Formulation
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$$TR_t = \max\left( H_t, C_{t-1} \right) - \min\left( L_t, C_{t-1} \right)$$
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### 2.2. Directional Movement Vectors ($+DM, -DM$)
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$$\Delta H_t = H_t - H_{t-1}, \quad\quad \Delta L_t = L_{t-1} - L_t$$
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$$+DM_t = \begin{cases} \Delta H_t, & \text{if } \Delta H_t > \Delta L_t \text{ and } \Delta H_t > 0 \\ 0.0, & \text{otherwise} \end{cases}$$
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$$-DM_t = \begin{cases} \Delta L_t, & \text{if } \Delta L_t > \Delta H_t \text{ and } \Delta L_t > 0 \\ 0.0, & \text{otherwise} \end{cases}$$
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---
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### 2.3. Wilder's Recursive Smoothing (RMA)
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For any series $X \in \{+DM, -DM, TR\}$, the initial seed is the cumulative sum over lookback period $P$:
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$$\text{Smoothed}(X)_P = \sum_{j=1}^{P} X_j$$
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Subsequent bars update via Wilder's recursive smoothing equation:
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$$\text{Smoothed}(X)_t = \text{Smoothed}(X)_{t-1} - \left( \frac{\text{Smoothed}(X)_{t-1}}{P} \right) + X_t = \frac{\text{Smoothed}(X)_{t-1} \cdot (P - 1) + X_t \cdot P}{P}$$
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---
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### 2.4. Directional Indicators ($+DI, -DI$)
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$$+DI_t = \left( \frac{\text{Smoothed}(+DM)_t}{\text{Smoothed}(TR)_t} \right) \times 100$$
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$$-DI_t = \left( \frac{\text{Smoothed}(-DM)_t}{\text{Smoothed}(TR)_t} \right) \times 100$$
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### 2.5. Directional Index ($DX$) & Average Directional Index ($ADX$)
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$$DX_t = \begin{cases} \left( \frac{|+DI_t - -DI_t|}{+DI_t + -DI_t} \right) \times 100, & \text{if } (+DI_t + -DI_t) > 0 \\ 0.0, & \text{otherwise} \end{cases}$$
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The final ADX curve begins at bar index $t_{\text{seed}} = 2P - 1$ as the arithmetic mean of the preceding $P$ values of $DX$:
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$$ADX_{2P-1} = \frac{1}{P} \sum_{j=0}^{P-1} DX_{2P-1-j}$$
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Subsequent values update via Wilder's smoothing on $DX$:
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$$ADX_t = \frac{ADX_{t-1} \cdot (P - 1) + DX_t}{P}$$
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---
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## 3. MQL5 Architecture & Engineering Standards
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```text
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┌────────────────────────────────────────────────────────┐
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│ DMI_Engine.mqh │
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│ (Core Math: Computes Smoothed TR, +DM, -DM, ±DI) │
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└──────────────────────────┬─────────────────────────────┘
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│ Feeds +DI & -DI Series
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▼
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┌────────────────────────────────────────────────────────┐
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│ ADX_Calculator.mqh │
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│ (DX Calculation & Wilder's Recursive ADX Engine) │
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└──────────────────────────┬─────────────────────────────┘
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│ Outputs ADX, +DI, -DI in O(1)
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▼
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┌────────────────────────────────────────────────────────┐
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│ ADX_Pro.mq5 │
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│ (Unified Wrapper: Native Timeframe & MTF Engine) │
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├──────────────────────────┬─────────────────────────────┤
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│ Direct Mode (O(1)) │ Synchronized MTF Pipeline │
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│ • Current Timeframe │ • DataSync_Tools Daemon │
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│ • 3 Output Plots │ • Staircase Flat-Force │
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└──────────────────────────┴─────────────────────────────┘
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```
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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.
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2. **Leak-Free Pointer Protection:** Factory methods (`CreateEngine`) explicitly verify pointer validity (`CheckPointer`) and safely free memory before re-allocation.
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3. **2026 MTF Framework with Staircase Solution:**
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* Asynchronous 1-second timer daemon (`OnTimerUpdate`) ensures higher-timeframe data synchronization without GUI freezes.
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* 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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---
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## 4. Parameters Reference
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### Timeframe Settings
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* `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.
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### ADX Core Settings
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* `InpPeriodADX` (*default: `14`*): Wilder's lookback smoothing period ($P$) for DMI and ADX calculations.
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* `InpCandleSource` (*default: `CANDLE_STANDARD`*): Candle price source (`CANDLE_STANDARD` or `CANDLE_HEIKIN_ASHI`).
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### Indicator Levels
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* `InpLevelTrend` (*default: `25.0`*): Key institutional trend strength threshold.
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* `InpLevelExtreme` (*default: `40.0`*): Strong trend / potential exhaustion boundary.
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* `InpLevelColor` (*default: `clrSilver`*): Color of horizontal level lines.
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* `InpLevelStyle` (*default: `STYLE_DOT`*): Line style of horizontal level lines.
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### Visual Settings
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* `InpColorADX` (*default: `clrDodgerBlue`*): ADX trend strength line color (Width: 2, Solid).
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* `InpColorPDI` (*default: `clrOliveDrab`*): +DI positive directional line color (Width: 1, Solid).
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* `InpColorNDI` (*default: `clrTomato`*): -DI negative directional line color (Width: 1, Solid).
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---
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## 5. Quantitative Trading Playbooks
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ ADX & DMI INSTITUTIONAL PLAYBOOKS │
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├────────────────────────────────────────────────────────────────────────┤
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│ 1. Regime Filter: ADX < 20 = No Trend / Chop (Pause Breakouts) │
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│ ADX > 25 = Valid Directional Trend Active │
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│ 2. Directional Trigger: +DI crosses above -DI while ADX > 25 = Buy │
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│ -DI crosses above +DI while ADX > 25 = Sell │
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│ 3. Climax Exhaustion: ADX > 40 turning downward = Scale Out Profits │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### 5.1. The ADX Regime Filter (Eliminating False Breakouts)
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* **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.
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* **Trend Confirmation ($ADX \ge 25.0$):** A rising ADX crossing above 25.0 confirms that institutional trend expansion is active.
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### 5.2. Directional Indicator Crossovers (+DI / -DI)
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* **Bullish Momentum Trigger:** `+DI` crosses above `-DI` AND `ADX > 25.0` (with ADX sloping upward) $\rightarrow$ High-probability Long Trend Entry.
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* **Bearish Momentum Trigger:** `-DI` crosses above `+DI` AND `ADX > 25.0` (with ADX sloping upward) $\rightarrow$ High-probability Short Trend Entry.
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### 5.3. Multi-Timeframe Macro Trend Strength Filter
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* Attach an **H1-calculated ADX** onto an **M5 execution chart**.
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* 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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---
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## 6. Indicator Buffer Map (For Developers & EA Integration)
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| Buffer Index | Name | Type | Description |
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| :---: | :---: | :--- | :--- |
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| **0** | `BufferADX` | `INDICATOR_DATA` | Average Directional Index (Main Trend Strength) |
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| **1** | `BufferPDI` | `INDICATOR_DATA` | Positive Directional Indicator (+DI) |
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| **2** | `BufferNDI` | `INDICATOR_DATA` | Negative Directional Indicator (-DI) |
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*All buffers strictly maintain non-series chronological order (`ArraySetAsSeries = false`), ensuring instant compatibility with Expert Advisors and scanner dashboards via `iCustom()`.*
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