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# Laguerre Momentum Professional
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## 1. Summary (Introduction)
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> **Part of the Laguerre Indicator Family**
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>
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> This indicator is a member of a family of tools based on John Ehlers' Laguerre filter.
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>
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> * [Laguerre Filter Pro](./Laguerre_Filter_Pro.md): A fast, responsive moving average.
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> * [Laguerre RSI Pro](./Laguerre_RSI_Pro.md): A smooth, noise-filtered momentum oscillator.
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> * **Laguerre Momentum Pro:** A Laguerre-smoothed oscillator of the bar-by-bar momentum.
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The Laguerre Momentum Pro is an oscillator that applies the powerful, low-lag **Laguerre Filter** to a **momentum source (Close - Open)** instead of the price.
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While the standard `Laguerre_Filter_Pro` provides a smoothed representation of the trend, this indicator isolates and smooths the raw bar-by-bar momentum. The `gamma` parameter allows the user to precisely control the trade-off between responsiveness and smoothness of the final oscillator.
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The result is a flexible, zero-mean oscillator that can be tuned to identify the underlying strength and direction of price velocity.
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## 2. Mathematical Foundations and Calculation Logic
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The indicator is a Laguerre-filtered average of the `Close - Open` value of each bar.
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### Calculation Steps (Algorithm)
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1. **Calculate Momentum Source:** For each bar, the source data is calculated as `Momentum = Close - Open`.
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2. **Apply Laguerre Filter:** A full, weighted Laguerre Filter is calculated on this `Momentum` data series, using the user-defined `gamma` to control the smoothing.
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## 3. MQL5 Implementation Details
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* **Unified Engine (`Laguerre_Engine.mqh`):** This indicator uses the exact same, powerful calculation engine as the `Laguerre_Filter_Pro` and `Laguerre_RSI_Pro`. The only difference is that it is initialized in `SOURCE_MOMENTUM` mode.
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* **Heikin Ashi Integration:** The indicator fully supports calculation on smoothed Heikin Ashi data (`HA Close - HA Open`).
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* **Stability via Full Recalculation:** The indicator employs a full recalculation on every `OnCalculate` call to ensure the stateful, recursive calculation is always stable.
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## 4. Parameters
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* **Gamma (`InpGamma`):** The Laguerre filter coefficient (0.0 to 1.0). This parameter controls the indicator's speed and smoothness.
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* **High Gamma (e.g., 0.7 - 0.9):** Results in a **slower, smoother** oscillator.
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* **Low Gamma (e.g., 0.1 - 0.3):** Results in a **faster, more volatile** oscillator.
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* **Candle Source (`InpCandleSource`):** Selects between `Standard` and `Heikin Ashi` candles for the `Close - Open` calculation.
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## 5. Usage and Interpretation
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The Laguerre Momentum is a classic zero-mean oscillator used for identifying momentum shifts and potential reversals.
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### Standalone Usage
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* **Zero-Line Crossover:**
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* A cross **above the zero line** indicates that bullish momentum is taking control.
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* A cross **below the zero line** indicates that bearish momentum is dominant.
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* **Divergence:**
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* **Bullish Divergence:** Price makes a **new lower low**, but the Laguerre Momentum makes a **higher low**.
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* **Bearish Divergence:** Price makes a **new higher high**, but the Laguerre Momentum makes a **lower high**.
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### Combined Strategy with Laguerre Filter (Primary Use)
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This oscillator is designed to be used in conjunction with its companion indicator, the `Laguerre_Filter_Pro`.
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* **The Zero-Cross Predicts the Filter's Turning Point:**
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* **Buy Signal:** When the **Laguerre Momentum** line crosses **above the zero line**, it provides a leading signal that the `Laguerre_Filter` on the main chart is forming a **trough (a bottom)**.
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* **Sell Signal:** When the **Laguerre Momentum** line crosses **below the zero line**, it provides a leading signal that the `Laguerre_Filter` is forming a **peak (a top)**.
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