mql5/Indicators/MyIndicators/MovingAverage_Pro_Documentation.md

Universal Moving Average (Moving Average) Pro (v3.00)

Quantitative Universal Smoothing Engine & Multi-Algorithm Moving Average Suite

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1. Summary (Introduction)

Moving Average Pro is the universal baseline trend overlay of the Professional MQL5 Suite. Built upon the core MovingAverage_Engine.mqh, it synthesizes eight classical, low-lag, and volume-weighted moving average algorithms into a single unified high-performance indicator.

Moving averages serve as the foundation for trend identification, dynamic support and resistance, and signal line smoothing across quantitative trading systems. Moving Average Pro provides instant algorithm interchangeability without altering indicator pipelines or charting architecture:

┌────────────────────────────────────────────────────────────────────────┐
│                   THE 8 MOVING AVERAGE ALGORITHMS                      │
├───────┬────────────────────────┬───────┬───────────────────────────────┤
│ Type  │ Full Mathematical Name │ Type  │ Full Mathematical Name        │
├───────┼────────────────────────┼───────┼───────────────────────────────┤
│ SMA   │ Simple Moving Average  │ TMA   │ Triangular Moving Average     │
│ EMA   │ Exponential Moving Avg │ DEMA  │ Double Exponential Moving Avg │
│ SMMA  │ Smoothed MA (Wilder)   │ TEMA  │ Triple Exponential Moving Avg │
│ LWMA  │ Linear Weighted MA     │ VWMA  │ Volume-Weighted Moving Avg    │
└───────┴────────────────────────┴───────┴───────────────────────────────┘

Key Capabilities

• 8 Native Smoothing Models: Seamlessly switch between linear, exponential, multi-stage zero-lag, and volume-weighted smoothing.
• Full Volume Routing (VWMA): Automatically queries broker SYMBOL_VOLUME_LIMIT to utilize Real Volume (VOLUME_REAL) or Tick Volume (VOLUME_TICK).
• Unified 2026 MTF Framework: Higher-timeframe moving averages (e.g., H1 or Daily 50/200 MAs) map onto lower-timeframe execution charts (M1, M5, M15) with flat, non-warping steps via DataSync_Tools.mqh.
• Synthetic Heikin Ashi Support: Computes smoothed curves from filtered Heikin Ashi price series via CMovingAverageCalculator_HA composition.
• State-Safe O(1) Recursive Execution: Stateful recursive smoothing registers (EMA, SMMA, DEMA, TEMA) update in zero latency on live market ticks.

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2. Mathematical Foundations & The 8 Smoothing Models

                  RAW INPUT SERIES: Close, Median, Typical, HA Close
                                           │
       ┌───────────────┬───────────────────┼───────────────────┬───────────────┐
       ▼               ▼                   ▼                   ▼               ▼
   Linear        Exponential           Double/Triple       Triangular       Volume-Weighted
  (SMA/LWMA)     (EMA/SMMA)            (DEMA/TEMA)           (TMA)              (VWMA)

2.1. Simple Moving Average (SMA)

Arithmetic mean of the previous P = \text{InpPeriod} bars:

\text{SMA}_t = \frac{1}{P} \sum_{j=0}^{P-1} P_{t-j}

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2.2. Exponential Moving Average (EMA)

First-order recursive Infinite Impulse Response (IIR) filter:

\alpha = \frac{2}{P + 1}, \quad\quad \text{EMA}_t = \alpha P_t + (1 - \alpha) \text{EMA}_{t-1}

The initial seed is computed as an SMA over the first P bars.

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2.3. Smoothed Moving Average (SMMA / Wilder's RMA)

J. Welles Wilder Jr.'s recursive smoothing algorithm (equivalent to an EMA with \alpha = 1/P):

\text{SMMA}_t = \frac{\text{SMMA}_{t-1} \cdot (P - 1) + P_t}{P}

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2.4. Linear Weighted Moving Average (LWMA)

Weights prices linearly proportional to their temporal recency:

W_j = P - j \text{LWMA}_t = \frac{\sum_{j=0}^{P-1} P_{t-j} \cdot (P - j)}{\sum_{j=0}^{P-1} (P - j)} = \frac{\sum_{j=0}^{P-1} P_{t-j} \cdot (P - j)}{\frac{P(P + 1)}{2}}

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2.5. Triangular Moving Average (TMA)

Double-smoothed simple moving average producing a triangular weighting kernel:

P_1 = \text{ceil}\left( \frac{P + 1}{2} \right), \quad\quad P_2 = P - P_1 + 1 \text{TMA}_t = \text{SMA}\left( \text{SMA}(P, P_1), P_2 \right)

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2.6. Double Exponential Moving Average (DEMA - Patrick Mulloy)

Eliminates first-order exponential phase lag:

\text{EMA1}_t = \text{EMA}(P, P), \quad\quad \text{EMA2}_t = \text{EMA}(\text{EMA1}, P) \text{DEMA}_t = 2 \cdot \text{EMA1}_t - \text{EMA2}_t

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2.7. Triple Exponential Moving Average (TEMA - Patrick Mulloy)

Eliminates second-order exponential phase lag for ultra-fast trend tracking:

\text{EMA1}_t = \text{EMA}(P, P), \quad \text{EMA2}_t = \text{EMA}(\text{EMA1}, P), \quad \text{EMA3}_t = \text{EMA}(\text{EMA2}, P) \text{TEMA}_t = 3 \cdot \text{EMA1}_t - 3 \cdot \text{EMA2}_t + \text{EMA3}_t

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2.8. Volume-Weighted Moving Average (VWMA)

Weights price bars directly proportional to transacted trade volume (V):

\text{VWMA}_t = \frac{\sum_{j=0}^{P-1} P_{t-j} \cdot V_{t-j}}{\sum_{j=0}^{P-1} V_{t-j}}

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2.9. Algorithm Selection & Performance Matrix

Algorithm	Smoothness	Phase Latency (Lag)	Noise Resistance	Optimal Market Context
SMA	Medium	High	High	Long-term macro benchmarks (e.g., 200 SMA).
EMA	High	Medium	Medium	General trend-following and MACD-style filtering.
SMMA	Very High	High	Very High	Wilder-style indicators (RSI, ADX, ATR).
LWMA	Medium	Low	Low	Short-term momentum tracking and signal lines.
TMA	Ultra-High	Very High	Ultra-High	Wave cycle analysis; filters all high frequencies.
DEMA	Medium	Very Low	Low	Fast trend trading; reduces 50% of EMA lag.
TEMA	Low	Near-Zero	Very Low	High-frequency scalping; eliminates almost all lag.
VWMA	High	Adaptive	High	Institutional liquidity analysis; volume-confirmed trends.

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3. MQL5 Architecture & Engineering Standards

┌────────────────────────────────────────────────────────┐
│                MovingAverage_Engine.mqh                │
│    (Core Universal Math: 8 MA Algorithms in O(1))      │
├──────────────────────────┬─────────────────────────────┤
│   Volume Routing Layer   │   Composition Engine        │
│   • Real Volume Support  │   • CMovingAverageCalc_HA   │
│   • Tick Volume Fallback │   • Dynamic Price Routing   │
└──────────────────────────┴─────────────────────────────┘
                           │ Outputs MA Series in O(1)
                           ▼
┌────────────────────────────────────────────────────────┐
│                 MovingAverage_Pro.mq5                  │
│    (Unified Wrapper: Native Timeframe & MTF Engine)    │
├──────────────────────────┬─────────────────────────────┤
│   Direct Mode (O(1))     │   Synchronized MTF Pipeline │
│   • Current Timeframe    │   • DataSync_Tools Daemon   │
│   • 1 Output Plot        │   • Staircase Flat-Force    │
└──────────────────────────┴─────────────────────────────┘

1. State-Safe Recursive Lifecycles: EMA, SMMA, DEMA, and TEMA calculators maintain persistent state registers without historical array corruption on live bar additions.
2. Unified Volume Routing: Automatically extracts real trade volume (CopyRealVolume) on supported exchange assets (Equities, Futures, Crypto) and seamlessly falls back to tick volume (CopyTickVolume) on Forex CFDs.
3. 2026 MTF Framework with Staircase Solution: Higher-timeframe moving averages map onto lower-timeframe execution charts with flat, synchronized steps via first_bar_of_forming_htf dynamic anchoring and DataSync_Tools.mqh.

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4. Parameters Reference

Timeframe Settings

• 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.

Moving Average Core Settings

• InpPeriod (default: 20): Lookback smoothing period (P).
• InpMAType (default: SMA): Mathematical algorithm selection (SMA, EMA, SMMA, LWMA, TMA, DEMA, TEMA, VWMA).
• InpSourcePrice (default: PRICE_CLOSE_STD): Input price series (Supports all 7 Standard and 7 Heikin Ashi modes).

Visual Settings

• InpColorMA (default: clrDodgerBlue): Line color.
• InpStyleMA (default: STYLE_SOLID): Line style (Solid, Dash, Dot).
• InpWidthMA (default: 2): Line thickness.

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5. Quantitative Trading Playbooks

┌────────────────────────────────────────────────────────────────────────┐
│                   MOVING AVERAGE TRADING PLAYBOOKS                     │
├────────────────────────────────────────────────────────────────────────┤
│ 1. Trend Baseline Retest: Pullbacks to rising EMA/VWMA offer low-risk  │
│                           continuation entries in strong markups.      │
│ 2. Institutional Cross:   50 EMA crossing above 200 SMA confirms a     │
│                           macro Golden Cross regime shift.             │
│ 3. MTF Macro Step Filter: Only execute M5 long setups when price is    │
│                           trading above the H1 50 EMA flat step.       │
└────────────────────────────────────────────────────────────────────────┘

5.1. Dynamic Support & Resistance Pullbacks

• Bullish Setup: Price is trending upward above a rising 20 EMA or 20 VWMA. When price pulls back to test the moving average line and prints a rejection wick \rightarrow High-conviction long continuation entry.
• Bearish Setup: Price is trending downward below a falling moving average line. Retests of the line from below offer short entry triggers.

5.2. Golden Cross & Death Cross Confirmation

• Golden Cross (Macro Bullish): Faster moving average (e.g., 50 EMA) crosses above a slower baseline (e.g., 200 SMA) \rightarrow Institutional confirmation of a long-term bull market.
• Death Cross (Macro Bearish): Faster moving average crosses below the slower baseline \rightarrow Institutional confirmation of a bear market.

5.3. Multi-Timeframe Macro Alignment Filter

• Attach an H1-calculated 50 EMA or H4-calculated 200 SMA onto an M5 execution chart.
• Rule: Only take intraday long trades when price is above the higher-timeframe flat step. This ensures zero counter-trend trading against macro institutional liquidity.

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

Buffer Index	Name	Type	Description
0	BufferMA	INDICATOR_DATA	Universal Moving Average Plot Line

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