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# Barbara Star's DMI Stochastic Oscillator Pro (v3.00)
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Quantitative Trend-Momentum Hybrid & Directional Stochastic Oscillator Suite
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---
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## 1. Summary (Introduction)
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**DMI Stochastic Pro** is an institutional-grade trend-momentum hybrid oscillator developed by technical analyst Barbara Star. It synthesizes **J. Welles Wilder Jr.'s Directional Movement System (+DI / -DI)** with **George Lane's Stochastic Oscillator formula**.
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Standard price-based Stochastics suffer from severe premature exhaustion in strong trends: because raw price continuously makes new highs, standard Stochastics gets pinned in "overbought" territory for extended periods. **Barbara Star resolved this by applying Stochastic normalization directly to the DMI Oscillator ($+DI - -DI$) rather than raw price**:
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* **Directional Balance ($50.0$ Level):** When %K is above $50.0$, buyers dominate the directional market structure (+DI > -DI). When %K is below $50.0$, sellers dominate (-DI > +DI).
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* **True Momentum Exhaustion ($\ge 80.0 / \le 20.0$):** Identifies when the relative dominance of buyers or sellers has reached a statistical local extreme and is beginning to decelerate.
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```text
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┌────────────────────────────────────────────────────────────────────────┐
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│ DMI STOCHASTIC HYBRID ARCHITECTURE │
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├──────────────────────┬────────────────────────┬────────────────────────┤
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│ Line Plot │ Color Code │ Core Role │
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├──────────────────────┼────────────────────────┼────────────────────────┤
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│ %K Main Line │ clrDodgerBlue (Width:2)│ Directional Momentum │
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│ %D Signal Line │ clrCoral (Width:1) │ Smoothed Trigger Line │
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└──────────────────────┴────────────────────────┴────────────────────────┘
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```
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### Key Capabilities
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* **0–100 Bounded Hybrid Scale:** Maps unbounded directional momentum into standardized institutional overbought/oversold bands.
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* **Flexible Dual-Engine Smoothing:** Independent Moving Average smoothing methods for both %K Slowing and %D Signal lines (supports SMA, EMA, SMMA, LWMA, TMA, DEMA, TEMA, and Volume-Weighted VWMA).
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* **Unified 2026 MTF Framework:** Higher-timeframe DMI Stochastic curves (e.g., H1 or H4) map onto lower-timeframe execution charts (M1, M5, M15) with flat, non-warping steps via `DataSync_Tools.mqh`.
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* **Synthetic Heikin Ashi Support:** Computes smoothed directional vectors from synthetic Heikin Ashi candles via `CDMIStochasticCalculator_HA`.
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* **Dynamic 5-Level Grid:** Fully customizable horizontal thresholds ($10, 20, 50, 80, 90$).
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---
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## 2. Mathematical Foundations & Hybrid Synthesis
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```text
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Wilder's DMI (+DI and -DI) over Period P_DMI
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│
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▼
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DMI Oscillator = (+DI) - (-DI) (Ranges: -100 to +100)
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│
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▼
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Stochastic Normalization over Fast %K Period (0 to 100)
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Fast %K = [ (DMI Osc - Lowest) / Range ] × 100
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│
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▼
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Slow %K = MA(Fast %K, Period = SlowK, Method = K_MA)
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│
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▼
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%D Signal = MA(Slow %K, Period = Smooth, Method = D_MA)
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```
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### 2.1. The DMI Difference Oscillator
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$$\text{DMI Oscillator}_t = \begin{cases} (+DI_t) - (-DI_t), & \text{if } \text{InpOscType} = \text{OSC\_PDI\_MINUS\_NDI} \\ (-DI_t) - (+DI_t), & \text{if } \text{InpOscType} = \text{OSC\_NDI\_MINUS\_PDI} \end{cases}$$
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---
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### 2.2. Fast %K Stochastic Normalization
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Across the lookback window $P_{\text{FastK}} = \text{InpFastKPeriod}$:
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$$\text{Highest}_t = \max_{j=0 \dots P_{\text{FastK}}-1} \left( \text{DMI Oscillator}_{t-j} \right)$$
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$$\text{Lowest}_t = \min_{j=0 \dots P_{\text{FastK}}-1} \left( \text{DMI Oscillator}_{t-j} \right)$$
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$$\text{Range}_t = \text{Highest}_t - \text{Lowest}_t$$
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$$\text{Fast \%K}_t = \begin{cases} \left( \frac{\text{DMI Oscillator}_t - \text{Lowest}_t}{\text{Range}_t} \right) \times 100, & \text{if } \text{Range}_t > 10^{-9} \\ 50.0, & \text{if } \text{Range}_t = 0 \end{cases}$$
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---
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### 2.3. Slow %K (Main Line) & %D (Signal Line) Smoothing
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The raw Fast %K is smoothed using the user-defined moving average algorithm ($\mathcal{MA}$):
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$$\text{\%K}_t = \mathcal{MA}\left( \text{Fast \%K}, \text{Period} = \text{InpSlowKPeriod}, \text{Type} = \text{InpStochMethod} \right)$$
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The final signal line is produced by smoothing the %K series:
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$$\text{\%D}_t = \mathcal{MA}\left( \text{\%K}, \text{Period} = \text{InpSmoothPeriod}, \text{Type} = \text{InpSignalMethod} \right)$$
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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 +DI and -DI Series) │
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└──────────────────────────┬─────────────────────────────┘
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│ Feeds +DI & -DI Series
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▼
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┌────────────────────────────────────────────────────────┐
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│ DMIStochastic_Calculator.mqh │
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│ (DMI Difference & Fast %K Stochastic Normalizer) │
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├──────────────────────────┬─────────────────────────────┤
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│ MovingAverage_Engine │ Dual MA Smoothing Engine │
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│ • Slow %K Calculator │ • %D Signal Calculator │
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└──────────────────────────┴─────────────────────────────┘
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│ Outputs %K and %D in O(1)
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▼
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┌────────────────────────────────────────────────────────┐
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│ DMIStochastic_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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│ • 2 Output Plots │ • Staircase Flat-Force │
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└──────────────────────────┴─────────────────────────────┘
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```
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1. **4-Tier Modular Hierarchy:** Isolates raw Directional Movement (`DMI_Engine.mqh`) from moving average smoothing (`MovingAverage_Engine.mqh`), orchestrated through `DMIStochastic_Calculator.mqh`.
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2. **Leak-Free Pointer Protection:** Factory methods (`CreateEngine`) safely delete previous engine instances before allocating new ones.
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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 UI lag.
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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 operates 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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### DMI & Stochastic Settings
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* `InpCandleSource` (*default: `CANDLE_STANDARD`*): Price source (`CANDLE_STANDARD` or `CANDLE_HEIKIN_ASHI`).
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* `InpOscType` (*default: `OSC_PDI_MINUS_NDI`*): Formula polarity (`OSC_PDI_MINUS_NDI` for Bullish-dominant scaling, `OSC_NDI_MINUS_PDI` for Bearish-dominant scaling).
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* `InpDMIPeriod` (*default: `10`*): Wilder's smoothing lookback period for DMI calculations.
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* `InpFastKPeriod` (*default: `10`*): Lookback period for Stochastic normalization.
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* `InpSlowKPeriod` (*default: `3`*): Smoothing period for the %K main line.
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* `InpStochMethod` (*default: `SMA`*): Smoothing method for %K (`SMA`, `EMA`, `SMMA`, `LWMA`, `TMA`, `DEMA`, `TEMA`, `VWMA`).
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* `InpSmoothPeriod` (*default: `3`*): Smoothing period for the %D signal line.
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* `InpSignalMethod` (*default: `SMA`*): Smoothing method for %D.
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### Indicator Levels (0–100 Range)
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* `InpLevelExtrHigh` (*default: `90.0`*): Extreme Overbought Climax boundary.
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* `InpLevelHigh` (*default: `80.0`*): Overbought Warning threshold.
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* `InpLevelMid` (*default: `50.0`*): Directional Equilibrium threshold (+DI = -DI).
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* `InpLevelLow` (*default: `20.0`*): Oversold Warning threshold.
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* `InpLevelExtrLow` (*default: `10.0`*): Extreme Oversold Climax 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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* `InpColorK` (*default: `clrDodgerBlue`*): %K line color (Width: 2, Solid).
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* `InpColorD` (*default: `clrCoral`*): %D signal 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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│ DMI STOCHASTIC TRADING PLAYBOOKS │
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├────────────────────────────────────────────────────────────────────────┤
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│ 1. 50-Line Equilibrium Cross: %K crossing > 50 confirms Bullish Flow. │
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│ %K crossing < 50 confirms Bearish Flow. │
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│ 2. Signal Crossover Trigger: %K crosses %D while in 20-80 zone in │
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│ direction of dominant trend. │
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│ 3. Deep Climax Reversal: %K exiting > 90 / < 10 extreme boundaries│
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│ signals exhaustion mean-reversion. │
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└────────────────────────────────────────────────────────────────────────┘
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```
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### 5.1. The 50-Level Directional Regime Filter
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* **Bullish Dominance:** When `%K > 50.0`, buyers hold directional control (+DI > -DI). Only take long setups.
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* **Bearish Dominance:** When `%K < 50.0`, sellers hold directional control (-DI > +DI). Only take short setups.
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### 5.2. Trend-Following Signal Line Crossovers (%K / %D)
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* **Bullish Continuation Trigger:** Price is in an established uptrend (Price > KAMA or 20 EMA), %K pulls back toward the 50.0 line, and crosses **above %D** $\rightarrow$ Enter Long.
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* **Bearish Continuation Trigger:** Price is in a downtrend, %K rallies toward 50.0, and crosses **below %D** $\rightarrow$ Enter Short.
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### 5.3. Multi-Timeframe Confluence Execution
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* Attach an **H1-calculated DMI Stochastic** onto an **M5 execution chart**.
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* **Rule:** Only take M5 long breakout/pullback entries when **H1 %K is above 50.0 and rising**. This eliminates counter-trend traps against higher-timeframe institutional 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** | `BufferK` | `INDICATOR_DATA` | DMI Stochastic %K (Main Directional Line) |
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| **1** | `BufferD` | `INDICATOR_DATA` | DMI Stochastic %D (Signal Trigger Line) |
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*Both buffers strictly maintain non-series chronological order (`ArraySetAsSeries = false`), ensuring instant compatibility with Expert Advisors and scanner dashboards via `iCustom()`.*
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