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124 lines
3.3 KiB
Markdown
124 lines
3.3 KiB
Markdown
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# TSI: True Strength Index
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The True Strength Index (TSI) is a momentum oscillator developed by William Blau that uses double-smoothed exponential moving averages of price momentum to reduce noise and identify trend strength and direction.
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## Historical Context
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William Blau introduced the TSI in his 1995 book "Momentum, Direction, and Divergence." The indicator was designed to provide a smoother momentum measure by applying double exponential smoothing to price changes, reducing the whipsaws common in simpler momentum indicators.
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## Algorithm and Implementation
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### 1. Momentum Calculation
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```csharp
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mom = Price - Price[1]
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absMom = |mom|
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```
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Price momentum captures the direction and magnitude of price change.
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### 2. Double EMA Smoothing
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```csharp
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// First smoothing with long period
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smoothedMomLong = EMA(mom, longPeriod)
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smoothedAbsMomLong = EMA(absMom, longPeriod)
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// Second smoothing with short period
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doubleSmoothedMom = EMA(smoothedMomLong, shortPeriod)
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doubleSmoothedAbsMom = EMA(smoothedAbsMomLong, shortPeriod)
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```
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Double smoothing reduces noise while preserving trend information.
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### 3. TSI Calculation
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```csharp
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TSI = 100 × doubleSmoothedMom / doubleSmoothedAbsMom
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```
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The ratio normalizes momentum to a percentage scale.
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### 4. Signal Line
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```csharp
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Signal = EMA(TSI, signalPeriod)
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```
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The signal line provides crossover signals.
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## Mathematical Formula
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### Core Formula
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$$TSI = 100 \times \frac{EMA(EMA(Price_t - Price_{t-1}, long), short)}{EMA(EMA(|Price_t - Price_{t-1}|, long), short)}$$
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### Signal Line
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$$Signal = EMA(TSI, signalPeriod)$$
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### Default Parameters
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- Long Period: 25
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- Short Period: 13
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- Signal Period: 13
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## Interpretation
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### Range
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- TSI oscillates between -100 and +100
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- Positive values indicate bullish momentum
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- Negative values indicate bearish momentum
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### Signals
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- **Zero Line Crossover**: TSI crossing above zero is bullish; below zero is bearish
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- **Signal Line Crossover**: TSI crossing above signal is bullish; below is bearish
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- **Divergence**: Price and TSI moving in opposite directions suggests trend reversal
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### Overbought/Oversold
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- Commonly used levels: +25/-25 or +30/-30
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- Extreme readings suggest potential reversal
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## Performance Characteristics
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### Operation Count (Streaming Mode)
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| Operation | Count |
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|-----------|-------|
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| Subtractions | 1 |
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| Absolute value | 1 |
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| EMA updates | 5 |
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| Division | 1 |
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| Multiplication | 1 |
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### Complexity
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- Time: O(1) per bar (streaming)
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- Space: O(1) - only EMA states maintained
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### Warmup Period
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warmupPeriod = longPeriod + shortPeriod + signalPeriod
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Default: 25 + 13 + 13 = 51 bars
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## Validation
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Cross-validated against:
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- TradingView's ta.tsi()
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- Stock.Indicators library
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- TA-Lib implementations
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## Common Pitfalls
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1. **Short Warmup**: Ensure sufficient warmup period for convergence
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2. **Division by Zero**: When no price movement, denominator approaches zero
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3. **Lag Inherent**: Double smoothing introduces lag in trend identification
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4. **Parameter Sensitivity**: Results vary significantly with period choices
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## References
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- Blau, William. "Momentum, Direction, and Divergence." Wiley, 1995
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- Blau, William. "True Strength Index." Technical Analysis of Stocks & Commodities, 1991
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- [TradingView TSI Documentation](https://www.tradingview.com/support/solutions/43000502302-true-strength-index-tsi/)
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