mql5/Indicators/MyIndicators/TSI_Pro.md

True Strength Index (TSI) Professional

1. Summary (Introduction)

The True Strength Index (TSI), developed by William Blau, is a momentum oscillator designed to provide a smoother and more reliable measure of market momentum. It fluctuates around a zero line, providing clear signals for trend direction, momentum, and overbought/oversold conditions.

Classic Definition: The original TSI is defined as a double-smoothed momentum indicator using two Exponential Moving Averages (EMAs).

Pro Features: Our TSI_Pro implementation extends this concept by allowing the calculation to be based on either standard or Heikin Ashi price data, and offers unprecedented customization by allowing traders to replace the standard EMAs with other smoothing methods (like SMA, DEMA, or TEMA).

2. Mathematical Foundations and Calculation Logic

The TSI is calculated by double-smoothing both the price momentum and the absolute price momentum, and then computing their ratio.

Required Components

• Slow Period (N_slow): The period for the first, longer-term smoothing (standard is 25).
• Fast Period (N_fast): The period for the second, shorter-term smoothing (standard is 13).
• Signal Period: The period for the moving average signal line.
• Source Price (P): The price series used for the calculation.

Calculation Steps (Algorithm)

1. Calculate Price Momentum: \text{Momentum}_i = P_i - P_{i-1}

2. First Smoothing (Slow Period): Apply an N_slow-period Moving Average to both the Momentum and its absolute value.

   • Classic TSI uses EMA here.

3. Second Smoothing (Fast Period): Apply an N_fast-period Moving Average to the results of the first smoothing step.

   • Classic TSI uses EMA here.

4. Calculate the TSI Value: Divide the double-smoothed momentum by the double-smoothed absolute momentum and scale the result to 100. \text{TSI}_i = 100 \times \frac{\text{MA}_{\text{fast}}(\text{MA}_{\text{slow}}(\text{Momentum}))_i}{\text{MA}_{\text{fast}}(\text{MA}_{\text{slow}}(\text{AbsMomentum}))_i}

5. Calculate the Signal Line: The signal line is a moving average of the TSI line itself.

3. MQL5 Implementation Details

Our MQL5 implementation follows a modern, component-based, object-oriented design.

• Full Engine Integration: The TSI calculator (TSI_Calculator.mqh) is a powerful orchestrator that utilizes five instances of our universal MovingAverage_Engine.mqh:

  1. Slow Momentum Engine: Smooths raw momentum.
  2. Fast Momentum Engine: Double-smooths the result.
  3. Slow Abs Momentum Engine: Smooths absolute momentum.
  4. Fast Abs Momentum Engine: Double-smooths the result.
  5. Signal Engine: Smooths the final TSI line. This architecture allows for extreme flexibility (e.g., using DEMA for internal smoothing) while maintaining code consistency.

• Optimized Incremental Calculation (O(1)): Unlike basic implementations that recalculate the entire history on every tick, this indicator employs an intelligent incremental algorithm.

  • State Tracking: It utilizes prev_calculated to process only new bars.
  • Persistent Buffers: Internal buffers persist their state between ticks.
  • Robust Offset Handling: The engine correctly handles the initialization periods of the chained calculations, ensuring that each step starts only when valid data is available.

• Object-Oriented Logic:

  • The Heikin Ashi version (CTSICalculator_HA) is achieved simply by instructing the main calculator to instantiate the Heikin Ashi version of the data preparation module.

4. Parameters

• TSI Calculation Settings:
  • InpSlowPeriod: The period for the first smoothing step. (Default: 25).
  • InpSlowMAType: The MA type for the first smoothing. Set to EMA for classic TSI behavior. (Default: EMA).
  • InpFastPeriod: The period for the second smoothing step. (Default: 13).
  • InpFastMAType: The MA type for the second smoothing. Set to EMA for classic TSI behavior. (Default: EMA).
  • InpSourcePrice: The source price for the calculation. (Standard or Heikin Ashi).
• Signal Line Settings:
  • InpSignalPeriod: The lookback period for the signal line. (Default: 13).
  • InpSignalMAType: The type of moving average for the signal line. (Default: EMA).

5. Usage and Interpretation

• Zero Line Crossovers: A crossover of the TSI line above the zero line indicates that long-term momentum has turned positive. A crossover below indicates negative momentum.
• Signal Line Crossovers: These provide earlier, shorter-term momentum signals. A bullish crossover is when the TSI line crosses above its signal line; a bearish crossover is the opposite.
• Overbought/Oversold Levels: The +25 and -25 levels are often used to identify extreme momentum.
• Divergence: Due to its smoothness, the TSI is excellent for spotting divergences between price and momentum, which can foreshadow reversals.