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77 lines
2.7 KiB
Markdown
77 lines
2.7 KiB
Markdown
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# TTM_LRC: TTM Linear Regression Channel
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> **Pending Implementation** - Placeholder for John Carter's TTM LRC indicator
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## Historical Context
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John Carter's TTM LRC (Linear Regression Channel) provides a clean, statistically-based price channel using linear regression analysis. Unlike Bollinger Bands which measure volatility around a moving average, LRC measures price deviation from the trend line, making it particularly useful for identifying overbought/oversold conditions within a defined trend.
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## Algorithm
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### Linear Regression Line
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```
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// Least squares regression over N periods
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slope = (N * ΣXY - ΣX * ΣY) / (N * ΣX² - (ΣX)²)
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intercept = (ΣY - slope * ΣX) / N
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midline = intercept + slope * (current_bar - start_bar)
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```
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### Standard Deviation Bands
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```
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residuals = close - linreg_value
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stddev = sqrt(Σ(residuals²) / N)
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upper_band_1 = midline + 1 * stddev
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lower_band_1 = midline - 1 * stddev
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upper_band_2 = midline + 2 * stddev
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lower_band_2 = midline - 2 * stddev
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```
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## Default Parameters
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| Parameter | Value | Description |
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|:----------|:------|:------------|
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| Length | 100 | Regression lookback period |
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| Deviations | 2.0 | Number of standard deviations for outer bands |
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| ShowMidline | true | Display the regression line |
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| ShowInnerBands | true | Display ±1σ bands |
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## Outputs
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| Output | Type | Description |
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|:-------|:-----|:------------|
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| Midline | double | Linear regression value (trend line) |
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| Upper1 | double | +1 standard deviation band |
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| Lower1 | double | -1 standard deviation band |
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| Upper2 | double | +2 standard deviation band |
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| Lower2 | double | -2 standard deviation band |
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| Slope | double | Current regression slope (trend direction) |
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| RSquared | double | Coefficient of determination (trend quality) |
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## Band Interpretation
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| Zone | Statistical Meaning | Trading Implication |
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|:-----|:--------------------|:--------------------|
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| Above +2σ | 2.5% probability | Extremely overbought |
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| +1σ to +2σ | 13.5% probability | Overbought |
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| -1σ to +1σ | 68% probability | Normal range |
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| -2σ to -1σ | 13.5% probability | Oversold |
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| Below -2σ | 2.5% probability | Extremely oversold |
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## Trading Strategy
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1. **Trend Following:** Trade in direction of slope when price bounces off midline
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2. **Mean Reversion:** Fade moves to ±2σ bands when R² is high
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3. **Breakout:** Watch for sustained moves beyond ±2σ as trend acceleration signals
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## Category
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**Channels** - Linear regression-based price channel with statistical deviation bands.
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## See Also
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- [REGCHANNEL: Linear Regression Channel](../regchannel/RegChannel.md)
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- [SDCHANNEL: Standard Deviation Channel](../sdchannel/SdChannel.md)
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- [BBANDS: Bollinger Bands](../bbands/Bbands.md)
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- [TTM_SQUEEZE: TTM Squeeze](../../dynamics/ttm_squeeze/TtmSqueeze.md)
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