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1995issue C071-2

Projection bands from high and low regression slopes

Highs and lows are fitted as two linear-regression slopes over a shared 14-bar lookback window, then advanced into projection bands. A scaled width reading, a location oscillator, and an exponentially smoothed oscillator are formed from those bands.

  • The high-side slope and the low-side slope are estimated separately over the same 14-bar lookback window by regressing highs and lows against sequential bar numbers.
  • The lower projection band is the smallest value among the current low and the prior 13 lows advanced by one through 13 multiples of the low-side slope.
  • The upper projection band is the largest value among the current high and the prior 13 highs advanced by one through 13 multiples of the high-side slope.
  • Projection bandwidth, the projection oscillator, and the slow projection oscillator are formed from those bands by a scaled width reading, a scaled close location, and exponential smoothing.
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Current trackLinear regression112 readingsExponential smoothing117 readings

From two slopes to bands and readings

The high-side slope and the low-side slope are fitted separately over one lookback window. Each slope is a linear-regression slope of highs or lows against sequential bar numbers. Those slopes then advance earlier highs and lows to the current bar to form the upper projection band and the lower projection band. Projection bandwidth, the projection oscillator, and the slow projection oscillator are formed from those two bands.

Separate slopes for highs and lows

Over a 14-bar lookback window, the low-side slope is the linear-regression slope of lows against sequential bar numbers in that window. Over the same 14-bar lookback window, the high-side slope is the linear-regression slope of highs against those sequential bar numbers.

The lookback window is a fixed count of sequential bars used to estimate each slope and to project earlier highs and lows forward.

How the projection bands are assembled

The lower projection band is the minimum of the current low and each of the prior 13 lows advanced by one through 13 multiples of the low-side slope. It is the smallest value among the current low and each earlier low advanced by the low-side slope times the number of bars to the current bar.

The upper projection band is the maximum of the current high and each of the prior 13 highs advanced by one through 13 multiples of the high-side slope. It is the largest value among the current high and each earlier high advanced by the high-side slope times the number of bars to the current bar.

Width, location, and a smoothed oscillator

Projection bandwidth equals 200 times the difference between the upper and lower bands, divided by the sum of those two bands. It is a scaled width reading that compares the gap between the two bands with their sum.

The projection oscillator equals 100 times the distance of the close above the lower band, divided by the distance between the upper and lower bands. It is a scaled location reading that places the close between the lower and upper bands.

The slow projection oscillator is an exponential moving average of the projection oscillator, using a smoothing factor of 2 divided by one plus the chosen smoothing length. It is an exponentially smoothed version of the projection oscillator.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
21 of 43 in the Linear regression track
19951-8 pp.Next on Linear regressionEvaluating a least-squares end-point moving average on a known test seriesA least-squares end-point moving average is the current end point of a straight-line fit to the lookback window, and the archive places that construction among other lookback smoothers rather than as a standalone market rule.
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  5. 1990Constructing least-squares polynomial smoothers
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  7. 1991Out-of-sample checks for linear growth fits
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  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
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  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
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  18. 1994Evaluating money supply as a linear leading-index baseline
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  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 year199575 readings
All 112 readings tagged Linear regression
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