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1995issue C021-8

Constructing least-squares trend channels

A trend channel can be built in three parts: a least-squares centerline on a window of closes, parallel bounds set by residual-spread, and a shared-price-scale so the fitted geometry can be checked on the same bars that built it.

  • A linear-regression fit through a window of closes returns one fitted value for each observation and supplies the trendline centerline.
  • Residual-spread is the population standard deviation of close minus fitted value on that same window, and it places parallel bounds two residual standard deviations above and below the centerline.
  • High-low-close-structure occupies the first price-axis group, while the fitted line and bands occupy a later overlay group that must use the same vertical range.
  • Dating the construction window on the category axis keeps the fitted line and bands aligned with the observation order used in the regression.
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Current trackLinear regression112 readingsTrendline128 readings

Three parts on the same bars

The construction treats a trendline as three parts that stay on the same bars: a centerline from linear-regression, parallel bounds from residual-spread, and a shared-price-scale that lets the fitted geometry be read against price.

A straight centerline through a window of closes can be produced with a least-squares fit that returns one fitted value for each observation in that window.

Fit the centerline with linear-regression

Linear-regression is a least-squares fit to an ordered window of closes. It supplies an explicit centerline baseline for the channel by returning one fitted value for each observation in that window.

Place bounds from residual-spread

Residual-spread is the dispersion of close minus fitted value over the same window used for the fit. Residual width is the population standard deviation of that difference, computed over the same observations used for the fit.

Parallel channel bounds can be placed two residual standard deviations above and below that centerline.

S&P 500 least-squares trend channel, Jan–May 1994

Daily S&P 500 closes from 3 January through late May 1994 sit inside a descending least-squares channel. The centerline is the linear-regression fit on those closes; the parallel overbought and oversold bounds sit two residual standard deviations above and below it. Values were read off the printed chart (Excel Figure 1 and the matching color overlay), not from a source table.
Daily S&P 500 closes from 3 January through late May 1994 sit inside a descending least-squares channel. The centerline is the linear-regression fit on those closes; the parallel overbought and oversold bounds sit two residual standard deviations above and below it. Values were read off the printed chart (Excel Figure 1 and the matching color overlay), not from a source table.S&P 500 · daily · 1994-01-03T00:00:00.000Z to 1994-05-31T00:00:00.000Z

Excel TREND on closes D2:D104 for 3 Jan–31 May 1994; bands are E±2·STDEVP(close−trend). Digitized from the raster, so prices are approximate to about one index point and the series is thinned to stay within 60 points.

Plot high-low-close-structure on a shared-price-scale

High-low-close-structure is the first plotted series group: highs, lows, and closes rendered as bars so the fitted geometry is read against actual price range, not against a line sketch of closes alone.

High, low, and close can occupy that first group on the price axis, while the fitted line and its offset bands occupy a later overlay group. Connecting strokes on the high and low series can be suppressed so the first group reads as high-low bars, with a distinct close mark on each bar.

Shared-price-scale is the rule that the overlay axis holding the fitted line and bands must use the same range as the high-low-close axis so the channel is not optically distorted. Splitting later series onto an overlay axis is required whenever those series live on a different numeric range than price, including a bounded oscillator.

Keep the window in observation order

The construction window can be dated on the category axis so the fitted line and bands stay aligned with the same observation order used in the regression.

Editorial reading

Editorial: the finished channel is read here as a trendline, a constructed centerline and offset bounds that later bars can confirm or break. That sentence is a TradersWeek interpretation of the historical workflow and is not an archive claim.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
19 of 43 in the Linear regression track
19951-8 pp.Next on Linear regressionLinear baseline holdout checks for annual bill-rate forecastsMany financial price and rate series moved with three-month bill yields, so they behaved as coincident series and supplied little lead.
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 fieldTrend and channels181 readingsBy year199575 readings
All 112 readings tagged Linear regression
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