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2003issue C011-11

How a rolling linear-regression endpoint is assembled as a moving-trend

A moving-trend series takes the current-bar endpoint of a linear-regression of close and can be drawn next to a moving-average and a weighted-moving-average so the three smoothers stay visible as construction choices.

  • A moving-trend is the current-bar value of a linear-regression of close over a fixed lookback, used as a price smoother rather than as a lagged average.
  • The same window can also produce a moving-average of close so both series can be drawn on one chart, and separate regressions of open, high, low, and close can be plotted as surrogate-bars.
  • A shorter linear-regression lookback, a weighted-moving-average written as a fixed combination of recent closes, and a spreadsheet with adjacent columns keep the construction differences in view.
  • The same moving-trend definition is also assembled as a closed-form sum over a 20-day window and as a least-squares end-point modifier on a 5-day window.
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Current trackWeighted moving average24 readingsLinear regression112 readingsMoving average449 readings

A smoother from the current-bar endpoint

A moving-trend is a rolling linear-regression endpoint used as a price smoother over a fixed lookback. The linear-regression is a least-squares fit to ordered price observations, and the current-bar endpoint becomes the filter value.

A moving-trend series can be built by taking the current-bar value of a linear-regression of close over a 20-bar lookback.

The same window as a moving-average

The same 20-bar window can also produce a simple moving-average of close so both smoothers can be drawn on one chart. The moving-average is an equal-weight average of prices over that lookback and is used as a baseline smoother.

Surrogate-bars from four regressions

Applying the same 20-bar regression separately to open, high, low, and close yields four series that can be plotted as surrogate-bars. Open, high, low, and close are each replaced by their own rolling regression endpoints so the result can be drawn as candles.

Shorter lookbacks of the same endpoint

A 7-bar linear-regression of close can be constructed in the same way as the 20-bar version for a shorter lookback comparison. A least-squares end-point modifier on a 5-day window is treated as equivalent to the moving-trend definition.

A weighted-moving-average on a short window

A 7-bar weighted filter can be written as a fixed linear combination of the current close and the prior six closes. A weighted-moving-average assigns more weight to recent prices than a simple average.

How platforms and a spreadsheet assemble the same idea

TradeStation implementations treat the moving-trend as a linear-regression smoother rather than a lagged average. An AIQ construction uses a 20-day window and a closed-form sum to obtain the moving-trend value from close.

One spreadsheet construction places a 20-bar simple average, a 20-bar linear-regression, and a 20-bar weighted-moving-average of close in adjacent columns.

Microsoft 20-bar moving trend versus 20-bar average

On daily Microsoft bars the 20-bar linear-regression endpoint turns with price while the same-length simple average lags through the mid-2002 swings. Dollar levels were read from the NeuroShell daily screenshot of Moving Trend(Close,20) against Avg(Close,20).
On daily Microsoft bars the 20-bar linear-regression endpoint turns with price while the same-length simple average lags through the mid-2002 swings. Dollar levels were read from the NeuroShell daily screenshot of Moving Trend(Close,20) against Avg(Close,20).MSFT · Daily · 2002-04-22T00:00:00.000Z to 2002-11-08T00:00:00.000Z

Both smoothers use the 20-bar window printed in the chart legend. Point values are visual readings from the labeled price scale, so turning levels are approximate to about a tenth of a dollar.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
17 of 20 in the Weighted moving average track
20041-11 pp.Next on Weighted moving averageConstructing a volume-weighted moving average as a forecast baselineA volume-weighted moving average sums each bar's price multiplied by that bar's volume over a chosen lookback, then divides by the total volume in the same lookback.
All readings on this track · 20 readings
  1. 1988Indicator smoothing: lookback, weight, and scale
  2. 1990Recency weighting in simple, linear, and exponential moving averages
  3. 1990Seed and recurrence construction for moving averages
  4. 1990Constructing a five-day step-weighted moving average
  5. 1992Constructing simple, weighted, and exponential moving averages
  6. 1992Constructing moving averages with weighting schemes and extra filters
  7. 1992Constructing a weighted-average TRIN10 with Bollinger envelopes
  8. 1992Constructing a banded weighted open-TRIN oscillator
  9. 1993Evaluating a weighted dual rate-of-change momentum filter
  10. 1993Constructing equal, linear and exponential moving averages
  11. 1993Constructing a general weighted moving average from one exponent
  12. 1993Calibrating the weighted-moving-average exponent
  13. 1993Constructing an exponent-weighted average of put-call ratios
  14. 1994Cycle-tuned momentum with spectral peaks
  15. 1999How a five-bar sine-weighted average is assembled
  16. 2003Same-scale trend filter from a rolling least-squares endpoint
  17. 2003How a rolling linear-regression endpoint is assembled as a moving-trend
  18. 2004Constructing a volume-weighted moving average as a forecast baseline
  19. 2005Constructing a move, volume and recency weighted average
  20. 2016MACD as a zero-line filter with dual moving averages
By fieldIndicators and filters682 readingsBy year2003104 readings
All 24 readings tagged Weighted moving average
Also on Weighted moving average5 readings
1982Constructing moving averages with weights, alignment, and adaptive lookbacks1988Indicator smoothing: lookback, weight, and scale1990Constructing a five-day step-weighted moving average1990Recency weighting in simple, linear, and exponential moving averages1990Seed and recurrence construction for moving averages