mql5/Indicators/MyIndicators/SMI_Pro.md

Stochastic Momentum Index (SMI) Pro

1. Summary (Introduction)

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.

The result is an oscillator that fluctuates around a zero line, providing clearer signals and minimizing erratic behavior.

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.

2. Mathematical Foundations and Calculation Logic

The SMI involves multiple layers of smoothing, using Exponential Moving Averages (EMAs).

Required Components

• %K Period: The lookback period for finding the highest high and lowest low.
• %D Period: The period for the double EMA smoothing.
• Signal Period: The period for the final EMA smoothing that creates the signal line.

Calculation Steps (Algorithm)

1. Find the Price Range: For each bar, determine the highest high and lowest low over the %K Period.
2. Calculate the Relative Distance: Determine the distance of the current close from the midpoint of the high-low range. \text{Relative Distance}_i = \text{Close}_i - \frac{\text{Highest High}_i + \text{Lowest Low}_i}{2}
3. First EMA Smoothing: Apply an EMA with the %D Period to both the Relative Distance and the Range.
4. Second EMA Smoothing: Apply another EMA with the %D Period to the results of the first smoothing.
5. Calculate the SMI Value: The final SMI is calculated as a percentage. \text{SMI}_i = 100 \times \frac{\text{EMA2(Relative)}_i}{\text{EMA2(Range)}_i / 2}
6. Calculate the Signal Line: The signal line is an EMA of the SMI line itself, using the Signal Period.

3. MQL5 Implementation Details

Our MQL5 implementation follows a modern, object-oriented design to ensure stability, reusability, and maintainability.

• Modular Calculation Engine (SMI_Calculator.mqh): The entire calculation logic is encapsulated within a reusable include file.

  • CSMICalculator: The base class that performs the full, multi-stage SMI calculation on a given set of High, Low, and Close prices.
  • 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.

• Optimized Incremental Calculation: Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm.

  • It utilizes the prev_calculated state to determine the exact starting point for updates.
  • 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.
  • This results in O(1) complexity per tick, ensuring instant updates and zero lag, even on charts with extensive history.

• 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.

4. Parameters

• %K Length (InpLengthK): The lookback period for finding the highest high and lowest low. Default is 10.
• %D Length (InpLengthD): The period used for the double EMA smoothing. Default is 3.
• EMA Length (InpLengthEMA): The smoothing period for the final signal line. Default is 3.
• Candle Source (InpCandleSource): Allows the user to select the candle type for the calculation (Standard or Heikin Ashi).

5. Usage and Interpretation

• Overbought/Oversold Levels: The SMI typically uses +40 as the overbought level and -40 as the oversold level.
• Crossovers:
  • 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.
  • 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.
• 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.
• Caution: While smoother than a standard Stochastic, the SMI is still a momentum oscillator and can give false signals in choppy markets.