mql5/Indicators/MyIndicators/TSI.md

True Strength Index (TSI) Indicator Family

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 by using a double-smoothing mechanism with Exponential Moving Averages (EMAs).

Our professional implementation is an indicator family consisting of two versions, both powered by a single, universal calculation engine:

• TSI_Pro: The classic implementation, displaying the main TSI line and a signal line.
• TSI_Oscillator_Pro: A histogram version that displays the difference between the TSI and its signal line, providing a clearer view of momentum acceleration/deceleration.

Both indicators support calculations based on either standard or Heikin Ashi price data.

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 EMA smoothing (standard is 25).
• Fast Period (N_fast): The period for the second, shorter-term EMA 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 EMA Smoothing (Slow Period): Apply an N_slow-period EMA to both the Momentum and its absolute value.
3. Second EMA Smoothing (Fast Period): Apply an N_fast-period EMA to the results of the first smoothing step.
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{EMA}_{\text{fast}}(\text{EMA}_{\text{slow}}(\text{Momentum}))_i}{\text{EMA}_{\text{fast}}(\text{EMA}_{\text{slow}}(\text{AbsMomentum}))_i}
5. Calculate the Signal Line: The signal line is a moving average of the TSI line itself.
6. Calculate the Oscillator (Histogram): The difference between the TSI and the Signal Line. \text{Oscillator}_i = \text{TSI}_i - \text{Signal}_i

3. MQL5 Implementation Details

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

• Centralized Calculation Engine (TSI_Calculator.mqh): The core of our implementation is a single, powerful calculation engine. This include file contains the complete, definition-true logic for calculating both the TSI and its signal line. It supports both standard and Heikin Ashi data sources through class inheritance (CTSICalculator and CTSICalculator_HA).

• 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.
  • Persistent State: The internal buffers (like m_ema1_mtm, m_ema2_mtm) persist their state between ticks. This allows the recursive EMA calculations to continue seamlessly from the last known value without re-processing the entire history.
  • This results in O(1) complexity per tick, ensuring instant updates and zero lag.

• Specialized Wrapper (TSI_Oscillator_Calculator.mqh): The oscillator indicator uses a thin "wrapper" class that utilizes the central engine. The wrapper's role is to:

  1. Instantiate the correct engine (standard or HA).
  2. Call the engine to get the calculated TSI and Signal lines.
  3. Perform one final step: calculate the difference between the two lines to produce the histogram. This approach ensures that both the TSI_Pro and TSI_Oscillator_Pro indicators are always based on the exact same core calculation logic.

• Composition with MA Engine: The TSI calculator internally uses our robust MovingAverage_Engine to calculate the Signal Line, ensuring consistency with other indicators.

4. Parameters

• Slow Period (InpSlowPeriod): The period for the first, longer-term EMA smoothing. Default is 25.
• Fast Period (InpFastPeriod): The period for the second, shorter-term EMA smoothing. Default is 13.
• Applied Price (InpSourcePrice): The source price for the calculation. This unified dropdown menu allows you to select from all standard and Heikin Ashi price types.
• Signal Line Settings:
  • InpSignalPeriod: The lookback period for the signal line. Default is 13.
  • InpSignalMAType: The type of moving average for the signal line. Default is MODE_EMA.

5. Usage and Interpretation

TSI_Pro (Line Chart)

• 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.

TSI_Oscillator_Pro (Histogram)

• Histogram > 0: The TSI is above its signal line (bullish momentum).
• Histogram < 0: The TSI is below its signal line (bearish momentum).
• Growing Histogram: Momentum is accelerating in the current direction.
• Shrinking Histogram: Momentum is decelerating, which can be an early warning of a potential crossover and trend change.