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2008issue C031-16

A linear-regression angle assembled as one trend filter

Price is smoothed with a moving average, a linear regression is fit to that series, and the slope is read as an angle with fixed degree bands. The construction is one trend filter rather than three separate indicators.

  • Price is first smoothed with a moving average, then a linear regression is fit to that cleaned series over a stated regression length.
  • The trend filter is the angle of that regression: rise over a slope-period run is converted with arctangent and scaled to degrees.
  • Default construction values include an 8-bar slope period and horizontal bands at plus 45, zero, and minus 45 degrees.
  • Editorial: read the smoother, the fitted slope, and the bands as one explicit trend filter rather than as three standalone indicators.
Entries in this reading3 entries
Current trackLinear regression112 readingsTrend filter137 readingsMoving average449 readings

The three named parts

A linear regression is a fitted line through a defined lookback of ordered prices whose slope becomes the forecast of local direction. A moving average is a smoother applied to price before the regression so the slope is taken from cleaned observations rather than raw ticks. A trend filter is a rule that converts the regression slope into an angle and keeps only those readings that clear preset ascent or descent bands.

Construction order

The construction first smooths price with a moving average, then fits a linear regression to that smoothed series over a stated regression length. The slope is taken from the cleaned series, not from the unsmoothed observations.

The filter is an angle

The trend filter is the angle of that regression. Rise over a slope-period run is converted with arctangent and scaled to degrees. Only readings that clear the preset ascent or descent bands are kept.

Default construction values

Default construction values include an 8-bar slope period and horizontal bands at plus 45, zero, and minus 45 degrees.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
37 of 43 in the Linear regression track
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All readings on this track · 43 readings
  1. 1990Constructing dollar baselines from rates, inflation, and residuals
  2. 1990Constructing a nominal index value from forward earnings and fitted yield
  3. 1990Constructing a nominal index price from earnings and a fitted yield
  4. 1990Endpoint-pinned price paths are not forecasts
  5. 1990Constructing least-squares polynomial smoothers
  6. 1991Endpoint growth rates versus linear-regression consistency
  7. 1991Out-of-sample checks for linear growth fits
  8. 1991Trend as persistence, not a straight line
  9. 1991Quadratic trend, residual oscillator, and a secondary cycle calendar
  10. 1991Time-origin offset and residual-price divergence on a quadratic least-squares fit
  11. 1991A least-squares trendline from ordered prices
  12. 1992Constructing log-linear growth and reliability screens
  13. 1992Constructing log-linear growth-rate baselines
  14. 1992Next-session high, low, and close from rolling linear regression
  15. 1993Auditing an index price-earnings multiple with short-rate regression
  16. 1994Regression-seeded nested exponential price filter
  17. 1994Constructing the double exponential average from lag cancellation
  18. 1994Evaluating money supply as a linear leading-index baseline
  19. 1995Constructing least-squares trend channels
  20. 1995Linear baseline holdout checks for annual bill-rate forecasts
  21. 1995Projection bands from high and low regression slopes
  22. 1995Evaluating a least-squares end-point moving average on a known test series
  23. 1996Constructing an endpoint moving average from a least-squares line
  24. 1996Scoring equity path consistency with a k-ratio overlay
  25. 1996Evaluating month-end yield gaps for equity regimes
  26. 1996Constructing session-indexed standard error bands
  27. 1998Evaluating linear regression baselines for index valuation
  28. 1998R-squared as a two-state trend filter from a price-time fit
  29. 2000Second-order moving-average lag correction
  30. 2002Price regression line versus beta for index tracking
  31. 2003Regression slope with an r-squared trend confidence gate
  32. 2003Constructing finite-volume-element divergence with slope comparison
  33. 2004Building a daily score from regression, retracement, and volume
  34. 2004Constructing least-squares trendlines from ordered prices
  35. 2007Rectangle breakout targets beyond height
  36. 2007Confirming a price trend with regression slope and r-squared
  37. 2008A linear-regression angle assembled as one trend filter
  38. 2010A two-state swing machine from four running extremes
  39. 2016Score oil-complex tightness before divergence or regression
  40. 2017Nikkei-yen intermarket divergence as a regime case study
  41. 2017Constructing Calmar ratio and linear regression baselines
  42. 2019Pair-trade layer construction versus average-spread management
  43. 2020A convolution slope built from nested linear regression
By fieldIndicators and filters682 readingsBy year200867 readings
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