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1995issue C101-8

Evaluating a least-squares end-point moving average on a known test series

A least-squares end-point moving average takes its current value from the end of a straight-line fit to the lookback window. This archive note shows how that construction was judged against ordinary moving averages on a known line-plus-turn sequence before a later market overlay was shown.

  • A 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.
  • On a constructed straight up-leg that peaked on day 26, an 11-day simple moving average stayed $5.00 below the series and turned down five days after the peak, while an 11-day exponential moving average sat $4.95 below by day 25 and reversed two days earlier than that simple average.
  • The matching 11-day end-point average tracked the same series from day 10 through day 25, peaked one day after the turn, then diverged for nine days with a largest gap of $2.55 on days 28 and 29.
  • Editorial reading: complete the known-sequence comparison first. A later market overlay belongs to the historical workflow and is not a reason to trust the overlay before the test series.
Entries in this reading3 entries
Least squares moving average3 readingsCurrent trackLinear regression112 readingsMoving average449 readings

What is being compared

This note explains how a least-squares end-point smoother can be judged against ordinary moving averages on a known line-plus-turn sequence. A moving average is a lookback smoother that reduces noise in ordered prices so an underlying trend can be compared across methods.

Linear regression, as used here, is a straight-line fit to a window of ordered observations. The least-squares moving average is the moving average whose current value is the end point of that fitted line.

A constructed line-plus-turn series

The archive used a constructed test series with a straight up-leg that peaked on day 26. An 11-day simple moving average stayed $5.00 below that up-leg and turned down five days after the series peaked.

An 11-day exponential moving average, started at the first price of zero, sat $4.95 below the test series by day 25 and reversed two days earlier than the matching simple moving average.

The 11-day end-point moving average is the end point of a least-squares straight line. On the same test series it matched prices from day 10 through day 25, then peaked one day after the series turned.

What happened after the turn

After the test series reversed, the 11-day end-point moving average diverged for nine days, with a largest gap of $2.55 on days 28 and 29.

A later market overlay in the same workflow

The archive also reported a 28-month Dow Jones Industrial Average overlay. A 200-day end-point moving average issued a sell 18 days earlier and 138 points higher than the earliest sell from the 200-day simple or exponential averages around the 1987 peak.

The same 200-day end-point overlay was reported to finish the September 1985 to October 1987 window with a 1025-point net, described as 2.33 times a buy-and-hold path over that interval.

Where the construction sits among smoothers

The archive reported a survey finding that 42 percent of catalogued technical indicators used a moving average in some form. That finding places the end-point construction among other lookback smoothers rather than as a standalone market rule.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
22 of 43 in the Linear regression track
19961-4 pp.Next on Linear regressionConstructing an endpoint moving average from a least-squares lineAn endpoint moving average is defined for every integer lookback of two or more observations as the last fitted value of a least-squares line of price against time.
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  22. 1995Evaluating a least-squares end-point moving average on a known test series
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  30. 2002Price regression line versus beta for index tracking
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  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
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  39. 2016Score oil-complex tightness before divergence or regression
  40. 2017Nikkei-yen intermarket divergence as a regime case study
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  42. 2019Pair-trade layer construction versus average-spread management
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By fieldIndicators and filters682 readingsBy year199575 readings
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