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Toh4iem9
64 lines
4.7 KiB
Markdown
64 lines
4.7 KiB
Markdown
# Stochastic Momentum Index (SMI) Pro
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## 1. Summary (Introduction)
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The Stochastic Momentum Index (SMI), developed by William Blau, is a smoother version of the standard Stochastic Oscillator. It measures the relationship between the closing price and the *midpoint* of its high-low range, rather than the closing price's position within the range.
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The result is an oscillator that fluctuates around a zero line, providing clearer signals and minimizing erratic behavior.
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Our `SMI_Pro` implementation is a unified, professional version that allows the calculation to be based on either **standard** or **Heikin Ashi** price data, selectable from a single input parameter.
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## 2. Mathematical Foundations and Calculation Logic
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The SMI involves multiple layers of smoothing, using Exponential Moving Averages (EMAs).
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### Required Components
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* **%K Period:** The lookback period for finding the highest high and lowest low.
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* **%D Period:** The period for the double EMA smoothing.
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* **Signal Period:** The period for the final EMA smoothing that creates the signal line.
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### Calculation Steps (Algorithm)
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1. **Find the Price Range:** For each bar, determine the highest high and lowest low over the `%K Period`.
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2. **Calculate the Relative Distance:** Determine the distance of the current close from the midpoint of the high-low range.
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$\text{Relative Distance}_i = \text{Close}_i - \frac{\text{Highest High}_i + \text{Lowest Low}_i}{2}$
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3. **First EMA Smoothing:** Apply an EMA with the `%D Period` to both the `Relative Distance` and the `Range`.
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4. **Second EMA Smoothing:** Apply another EMA with the `%D Period` to the results of the first smoothing.
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5. **Calculate the SMI Value:** The final SMI is calculated as a percentage.
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$\text{SMI}_i = 100 \times \frac{\text{EMA2(Relative)}_i}{\text{EMA2(Range)}_i / 2}$
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6. **Calculate the Signal Line:** The signal line is an EMA of the SMI line itself, using the `Signal Period`.
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## 3. MQL5 Implementation Details
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Our MQL5 implementation follows a modern, object-oriented design to ensure stability, reusability, and maintainability.
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* **Modular Calculation Engine (`SMI_Calculator.mqh`):**
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The entire calculation logic is encapsulated within a reusable include file.
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* **`CSMICalculator`**: The base class that performs the full, multi-stage SMI calculation on a given set of High, Low, and Close prices.
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* **`CSMICalculator_HA`**: A child class that inherits all the complex logic and only overrides the initial data preparation step to use smoothed Heikin Ashi prices as its input. This object-oriented approach eliminates code duplication.
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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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* The internal buffers (`m_ema_rel`, `m_ema_range`, etc.) persist their state between ticks, allowing the recursive EMA algorithms to continue seamlessly from the last known value.
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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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* **Robust EMA Initialization:** Each recursive EMA calculation step is carefully initialized with a simple average to provide a stable starting point for the calculation chain and prevent floating-point overflows.
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## 4. Parameters
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* **%K Length (`InpLengthK`):** The lookback period for finding the highest high and lowest low. Default is `10`.
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* **%D Length (`InpLengthD`):** The period used for the double EMA smoothing. Default is `3`.
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* **EMA Length (`InpLengthEMA`):** The smoothing period for the final signal line. Default is `3`.
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* **Candle Source (`InpCandleSource`):** Allows the user to select the candle type for the calculation (`Standard` or `Heikin Ashi`).
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## 5. Usage and Interpretation
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* **Overbought/Oversold Levels:** The SMI typically uses +40 as the overbought level and -40 as the oversold level.
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* **Crossovers:**
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* **SMI / Signal Line Crossover:** When the SMI line crosses above its signal line, it can be considered a bullish signal. When it crosses below, it's a bearish signal.
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* **Zero Line Crossover:** A crossover of the SMI line above the zero line indicates that bullish momentum is taking control. A crossover below zero indicates bearish momentum.
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* **Divergence:** Look for divergences between the SMI and the price. A bearish divergence (higher price highs, lower SMI highs) can signal a potential top, while a bullish divergence (lower price lows, higher SMI lows) can signal a potential bottom.
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* **Caution:** While smoother than a standard Stochastic, the SMI is still a momentum oscillator and can give false signals in choppy markets.
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