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Toh4iem9
124 lines
7.2 KiB
Markdown
124 lines
7.2 KiB
Markdown
# Moving Average Pro
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## 1. Summary (Introduction)
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The `MovingAverage_Pro` is a universal, "all-in-one" moving average indicator designed for maximum flexibility and efficiency. It consolidates **seven** fundamental and advanced moving average types into a single, powerful tool, allowing the user to switch between them with a simple dropdown menu.
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The available moving average types are:
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* **SMA** (Simple Moving Average)
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* **EMA** (Exponential Moving Average)
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* **SMMA** (Smoothed Moving Average)
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* **LWMA** (Linear Weighted Moving Average)
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* **TMA** (Triangular Moving Average)
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* **DEMA** (Double Exponential Moving Average)
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* **TEMA** (Triple Exponential Moving Average)
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As part of our professional indicator suite, it fully supports calculations on either **standard** or **Heikin Ashi** price data, providing a consistent and powerful tool for any analysis style.
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## 2. Mathematical Foundations and Calculation Logic
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Each moving average type offers a different balance between smoothing and responsiveness. Our implementation is "definition-true" to the standard formulas used in technical analysis.
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### SMA (Simple Moving Average)
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The SMA is an unweighted arithmetic mean of the last `N` prices. It gives equal weight to all data points, resulting in a smooth line ideal for identifying long-term trends.
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$\text{SMA}_t = \frac{1}{N} \sum_{i=0}^{N-1} P_{t-i}$
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Where:
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* $P_t$ is the price at the current bar.
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* $N$ is the moving average period.
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### EMA (Exponential Moving Average)
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The EMA is a weighted average that applies more weight to recent prices, making it react more quickly to new information. It is calculated recursively.
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The smoothing factor, `alpha` ($\alpha$), is calculated as:
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$\alpha = \frac{2}{N + 1}$
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The EMA is then calculated as:
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$\text{EMA}_t = (P_t \times \alpha) + (\text{EMA}_{t-1} \times (1 - \alpha))$
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* **Initialization:** The first value of the EMA series ($\text{EMA}_{N-1}$) is calculated as a Simple Moving Average of the first `N` prices.
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### SMMA (Smoothed Moving Average)
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The SMMA, also known as Wilder's Smoothing, is a specialized moving average with a longer "memory" than an EMA. It is also calculated recursively and is ideal for filtering out market noise.
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The formula is:
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$\text{SMMA}_t = \frac{(\text{SMMA}_{t-1} \times (N-1)) + P_t}{N}$
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* **Initialization:** Similar to the EMA, the first value of the SMMA series is calculated as a Simple Moving Average of the first `N` prices.
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### LWMA (Linear Weighted Moving Average)
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The LWMA applies linearly more weight to recent prices. The most recent price gets the highest weight, and the weight decreases linearly for older prices.
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The formula is:
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$\text{LWMA}_t = \frac{\sum_{i=0}^{N-1} P_{t-i} \times (N-i)}{\sum_{j=1}^{N} j}$
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Where the denominator is the sum of the weights (e.g., for a 3-period LWMA, the weights are 3, 2, 1, and the sum is 6).
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### TMA (Triangular Moving Average)
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The TMA is a double-smoothed moving average that gives the most weight to the data in the middle of its lookback period. It is extremely smooth and is best used as a long-term trendline or cyclical centerline, not for fast signals. It is calculated by taking an SMA of an SMA.
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1. $\text{SMA}_{1_t} = \text{SMA}(P, \text{Ceiling}(\frac{N + 1}{2}))_t$
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2. $\text{TMA}_t = \text{SMA}(\text{SMA}_1, \text{Floor}(\frac{N + 1}{2}))_t$
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### DEMA (Double Exponential Moving Average)
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Developed by Patrick Mulloy, the DEMA is not a simple double-smoothed EMA. It is a lag-reduction technique that combines a single EMA and a double EMA to create a more responsive moving average.
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1. $\text{EMA}_{1_t} = \text{EMA}(P, N)_t$
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2. $\text{EMA}_{2_t} = \text{EMA}(\text{EMA}_1, N)_t$
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3. $\text{DEMA}_t = (2 \times \text{EMA}_{1_t}) - \text{EMA}_{2_t}$
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### TEMA (Triple Exponential Moving Average)
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Also developed by Patrick Mulloy, the TEMA is an even more advanced lag-reduction technique that uses a triple-smoothing process to create an extremely responsive moving average that stays very close to the price.
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1. $\text{EMA}_{1_t} = \text{EMA}(P, N)_t$
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2. $\text{EMA}_{2_t} = \text{EMA}(\text{EMA}_1, N)_t$
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3. $\text{EMA}_{3_t} = \text{EMA}(\text{EMA}_2, N)_t$
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4. $\text{TEMA}_t = (3 \times \text{EMA}_{1_t}) - (3 \times \text{EMA}_{2_t}) + \text{EMA}_{3_t}$
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## 3. MQL5 Implementation Details
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* **Universal Calculation Engine (`MovingAverage_Engine.mqh`):**
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The entire calculation logic for all **seven** MA types is encapsulated within a single, reusable engine file. This centralized approach eliminates code duplication and simplifies maintenance.
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* **Optimized Incremental Calculation:**
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Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm.
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* It utilizes the `prev_calculated` state to determine the exact starting point for updates.
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* **Persistent State:** For recursive types (EMA, SMMA) and complex types (DEMA, TEMA), the internal intermediate buffers (e.g., `ema1`, `ema2`) persist their state between ticks. This allows the calculation to continue seamlessly from the last known value without re-processing the entire history.
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* This results in **O(1) complexity** per tick, ensuring instant updates and zero lag, even on charts with extensive history.
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* **Efficient EMA Calculation:** The engine uses a dedicated `CalculateEMA` helper function that supports incremental updates. This function is called recursively to efficiently build the DEMA and TEMA.
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* **User-Selectable Type via Enum:** The indicator uses an `input ENUM_MA_TYPE` parameter, which creates a user-friendly dropdown menu in the settings window. The user's selection is passed directly to the universal engine.
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* **Object-Oriented Design (Inheritance):** A `CMovingAverageCalculator` base class and a `CMovingAverageCalculator_HA` derived class are used to cleanly separate the logic for standard and Heikin Ashi price sources.
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* **Dynamic Naming:** The indicator's name on the chart automatically updates to reflect the user's current selections (e.g., "DEMA HA(50)", "TMA(100)").
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## 4. Parameters
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* **Period (`InpPeriod`):** The lookback period for the moving average calculation.
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* **MA Type (`InpMAType`):** A dropdown menu to select the desired moving average type (SMA, EMA, SMMA, LWMA, TMA, DEMA, TEMA).
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* **Applied Price (`InpSourcePrice`):** The source price for the calculation.
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## 5. Usage and Interpretation
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Moving averages are one of the most fundamental tools in technical analysis.
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* **Trend Identification:** The primary use is to identify the direction of the trend.
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* When the price is consistently above the moving average and the line is sloping upwards, the trend is considered bullish.
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* When the price is consistently below the moving average and the line is sloping downwards, the trend is considered bearish.
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* **Dynamic Support and Resistance:** In a trending market, the moving average line itself often acts as a dynamic level of support (in an uptrend) or resistance (in a downtrend), providing potential entry points on pullbacks.
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* **Crossover Signals:** A common strategy involves using two instances of the `MovingAverage_Pro` indicator with different periods (e.g., a fast 50-period EMA and a slow 200-period EMA).
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* A "Golden Cross" (fast MA crosses above slow MA) is a bullish signal.
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* A "Death Cross" (fast MA crosses below slow MA) is a bearish signal.
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