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Toh4iem9
92 lines
5.3 KiB
Markdown
92 lines
5.3 KiB
Markdown
# True Strength Index (TSI) Indicator Family
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## 1. Summary (Introduction)
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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.
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Our professional implementation is an **indicator family** consisting of two versions, both powered by a single, universal calculation engine:
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* **`TSI_Pro`:** The classic implementation, displaying the main TSI line and a signal line.
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* **`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.
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**Pro Features:** Both indicators support calculations based on either **standard** or **Heikin Ashi** price data, and offer unprecedented customization by allowing traders to replace the standard EMAs with other smoothing methods (like SMA, DEMA, or TEMA) for every step of the calculation.
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## 2. Mathematical Foundations and Calculation Logic
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The TSI is calculated by double-smoothing both the price momentum and the absolute price momentum, and then computing their ratio.
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### Required Components
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* **Slow Period (N_slow):** The period for the first, longer-term smoothing (standard is 25).
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* **Fast Period (N_fast):** The period for the second, shorter-term smoothing (standard is 13).
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* **Signal Period:** The period for the moving average signal line.
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* **Source Price (P):** The price series used for the calculation.
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### Calculation Steps (Algorithm)
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1. **Calculate Price Momentum:** $\text{Momentum}_i = P_i - P_{i-1}$
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2. **First Smoothing (Slow Period):** Apply an `N_slow`-period Moving Average to both the `Momentum` and its absolute value.
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* *Classic TSI uses EMA here.*
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3. **Second Smoothing (Fast Period):** Apply an `N_fast`-period Moving Average to the results of the first smoothing step.
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* *Classic TSI uses EMA here.*
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4. **Calculate the TSI Value:** Divide the double-smoothed momentum by the double-smoothed absolute momentum and scale the result to 100.
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$\text{TSI}_i = 100 \times \frac{\text{MA}_{\text{fast}}(\text{MA}_{\text{slow}}(\text{Momentum}))_i}{\text{MA}_{\text{fast}}(\text{MA}_{\text{slow}}(\text{AbsMomentum}))_i}$
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5. **Calculate the Signal Line:** The signal line is a moving average of the TSI line itself.
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6. **Calculate the Oscillator (Histogram):** The difference between the TSI and the Signal Line.
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$\text{Oscillator}_i = \text{TSI}_i - \text{Signal}_i$
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## 3. MQL5 Implementation Details
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Our MQL5 implementation follows a modern, component-based, object-oriented design.
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* **Full Engine Integration:**
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The core TSI calculator (`TSI_Calculator.mqh`) is a powerful orchestrator that utilizes **five** instances of our universal `MovingAverage_Engine.mqh`:
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1. **Slow Momentum Engine:** Smooths raw momentum.
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2. **Fast Momentum Engine:** Double-smooths the result.
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3. **Slow Abs Momentum Engine:** Smooths absolute momentum.
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4. **Fast Abs Momentum Engine:** Double-smooths the result.
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5. **Signal Engine:** Smooths the final TSI line.
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This architecture allows for extreme flexibility while maintaining code consistency.
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* **Optimized Incremental Calculation (O(1)):**
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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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* **State Tracking:** It utilizes `prev_calculated` to process only new bars.
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* **Persistent Buffers:** Internal buffers persist their state between ticks.
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* **Robust Offset Handling:** The engine correctly handles the initialization periods of the chained calculations.
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* **Composition Pattern (Oscillator):**
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The `TSI_Oscillator_Calculator` uses composition instead of inheritance. It internally owns and manages an instance of the main `CTSICalculator`. This ensures that the Oscillator version uses exactly the same mathematical logic as the Line version, guaranteeing 100% consistency.
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## 4. Parameters
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* **TSI Calculation Settings:**
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* `InpSlowPeriod`: The period for the first smoothing step. (Default: `25`).
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* `InpSlowMAType`: The MA type for the first smoothing. Set to **EMA** for classic TSI behavior. (Default: `EMA`).
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* `InpFastPeriod`: The period for the second smoothing step. (Default: `13`).
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* `InpFastMAType`: The MA type for the second smoothing. Set to **EMA** for classic TSI behavior. (Default: `EMA`).
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* `InpSourcePrice`: The source price for the calculation. (Standard or Heikin Ashi).
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* **Signal Line Settings:**
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* `InpSignalPeriod`: The lookback period for the signal line. (Default: `13`).
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* `InpSignalMAType`: The type of moving average for the signal line. (Default: `EMA`).
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## 5. Usage and Interpretation
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### `TSI_Pro` (Line Chart)
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* **Zero Line Crossovers:** A crossover of the TSI line above the zero line indicates that long-term momentum has turned positive.
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* **Signal Line Crossovers:** These provide earlier, shorter-term momentum signals.
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* **Overbought/Oversold Levels:** The **+25 and -25** levels are often used to identify extreme momentum.
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* **Divergence:** Excellent for spotting divergences between price and momentum.
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### `TSI_Oscillator_Pro` (Histogram)
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* **Histogram > 0:** The TSI is above its signal line (bullish momentum).
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* **Histogram < 0:** The TSI is below its signal line (bearish momentum).
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* **Growing Histogram:** Momentum is accelerating.
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* **Shrinking Histogram:** Momentum is decelerating (potential reversal warning).
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