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Linear Regression Channel

Statistical Intermediate

OLS-fit a trend line over a rolling window; trade when price breaks outside its confidence band.

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Strategy briefing

Understand what this strategy is actually betting on before you touch the parameter panel.

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Start with the intuition
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Use category and difficulty as context
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Compare before optimizing
Compare peers Methodology notes
01
Map the strategy to a regime thesis
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Read the math as a constraint system
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Use parameters to test fragility, not creativity
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Learning linkup

Read the model brief like a skeptic

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The Intuition

The Linear Regression Channel strategy fits an Ordinary Least Squares (OLS) trend line to a rolling window of prices, then builds confidence-band channels around that trend line using the standard deviation of residuals. The strategy is long when price falls below the lower band (overshooting below the trend) and short when price rises above the upper band (overshooting above the trend).

Compared to Bollinger Bands, the LR Channel is more sophisticated: Bollinger Bands build the channel around a flat rolling mean, while the LR Channel builds it around a fitted trend line. This means in a trending market, the LR Channel correctly identifies the trend direction and only signals mean reversion when prices deviate from the trend — not from a flat level. In uptrending markets, this reduces the number of false short signals that plague simple Bollinger Bands.

The residual standard deviation serves as the volatility-adaptive bandwidth, similar to Bollinger Bands. When the price has been oscillating widely around the trend (large residuals), the bands are wide — fewer signals, but each represents a more extreme deviation. When the price has been tracking the trend closely (small residuals), the bands are narrow — more signals, but each represents a moderate deviation.

Key assumptions: (1) Price within the lookback window follows a linear trend — the OLS regression is a meaningful characterisation of the recent price path. If the trend is nonlinear (e.g., exponential growth), the residuals will be biased and the channel will be poorly calibrated. (2) Deviations from the fitted trend are mean-reverting rather than accumulating. (3) The slope and intercept estimated in the lookback window are predictive of the short-term future direction of the trend.

The strategy can fail when the linear trend breaks abruptly — a structural break in price (earnings surprise, major macro event) causes the price to move to a new level that is outside the channel permanently. The strategy will repeatedly signal "reversion" while the price continues to move in the new direction. Filtering signals by trend direction — only taking long signals in uptrending markets (positive OLS slope) and short signals in downtrending markets — can significantly reduce this failure mode.

The Math

Read this as a compact model summary: what the signal sees, what it ignores, and where fragility can creep in.

OLS fit over Close[t-n : t]:
  predicted(t) = slope × (n-1) + intercept
  residuals    = Close[i] - (slope × i + intercept)
  std_resid    = std(residuals)
  Upper(t)     = predicted(t) + k × std_resid
  Lower(t)     = predicted(t) - k × std_resid

Signal(t) = +1  if Close(t) < Lower(t)
          = -1  if Close(t) > Upper(t)

Parameters

ParameterTypeDefaultDescription
window int 30 Rolling OLS regression window (days)
num_std float 2.0 Number of residual std devs for band width

Source Code

Live source — fetched from engine/strategies/lr_channel.py

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Further Reading

  • Raschke, L. & Connors, L. (1995). Street Smarts. M. Gordon Publishing.
  • Elder, A. (2002). Come Into My Trading Room. Wiley.
  • Kaufman, P. (2013). Trading Systems and Methods, 5th ed. Wiley.
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