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1994issue C061

Constructing a composite from weighted, smoothed rate-of-change windows

The indicator is assembled in three operations: four zero-centered rate-of-change series, an independent simple or exponential moving average on each series, and a weighted sum that gives the longest window the largest integer weight. Archive recipes fix those choices for daily, weekly and monthly sampling.

  • The indicator is assembled in three operations: compute four rate-of-change series, smooth each series with a simple or exponential moving average, then form a weighted sum of the smoothed series.
  • Each rate-of-change divides the current close by the close a fixed number of periods earlier, multiplies by 100 and subtracts 100, so the series is centered on zero.
  • A moving average is applied independently to each window. Exponential smoothing uses the smoothing-constant 2/(n+1); a 3-period span uses 0.50, and the first observation seeds the average.
  • Composite-weighting then uses 1, 2, 3 and 4 so the longest window contributes the most. Parameter sets exist for daily, weekly and monthly sampling, including a long-term weekly set of rate-of-change lengths 39, 52, 78 and 104.
Entries in this reading3 entries
Current trackRate of Change50 readingsExponential smoothing117 readingsMoving average449 readings

Three operations

The indicator is assembled in three operations. Compute four rate-of-change series. Smooth each series with a simple or exponential moving average. Then form a weighted sum of the smoothed series.

Four zero-centered rate-of-change windows

A rate-of-change is a momentum reading that divides the latest close by the close a fixed number of periods earlier, scales the ratio by 100, and subtracts 100 so the series is centered on zero. The construction uses four such series, each with its own lookback.

One short-term weekly recipe uses rate-of-change lengths 3, 4, 6 and 10. Parameter sets are also specified for daily and monthly sampling, and a long-term weekly set uses rate-of-change lengths 39, 52, 78 and 104.

A moving average on each window

A moving average is a simple or exponential smoother applied independently to each rate-of-change window before those windows are weighted and added. Exponential smoothing is a recursive average that blends the newest observation with the prior average using a constant equal to 2 divided by one more than the span.

The smoothing-constant is the update fraction 2/(n+1) that sets how quickly an exponential average responds when the span is n. A 3-period span therefore uses 0.50. The exponential update adds the smoothing-constant times the gap between the new observation and the prior average. The first observation seeds the average and smoothing begins on the following bar.

The short-term weekly recipe uses exponential spans 3, 4, 6 and 8. In the weekly construction walk-through, the 4-, 6- and 8-period exponential constants appear as 0.4, 0.29 and 0.22.

Composite-weighting after the smoothers

Composite-weighting is the final sum in which four independently smoothed momentum windows receive increasing integer weights so the longest window contributes the most. After smoothing, the four series are combined as one times the shortest window plus two, three and four times the successively longer windows. The short-term weekly recipe uses weights 1, 2, 3 and 4.

Parameter sets are specified for daily, weekly and monthly sampling and for both simple and exponential smoothing.

Four weekly S&P 500 rate-of-change windows used to assemble short-term KST

Each series is a zero-centered weekly rate of change on the S&P 500, so a trader can see the four lookbacks disagree in both size and sign before any smoother or weight is applied. The 3-week window swings first; the 10-week window stays negative through the March–April slide and only turns up in May. Every point is the exact cell value from the source short-term weekly spreadsheet, not a reading off a plotted curve.
Each series is a zero-centered weekly rate of change on the S&P 500, so a trader can see the four lookbacks disagree in both size and sign before any smoother or weight is applied. The 3-week window swings first; the 10-week window stays negative through the March–April slide and only turns up in May. Every point is the exact cell value from the source short-term weekly spreadsheet, not a reading off a plotted curve.S&P 500 · Weekly · 1992-01-17T00:00:00.000Z to 1992-05-08T00:00:00.000Z

Short-term weekly recipe from the parameter table: 3-, 4-, 6- and 10-week ROC. The printed spreadsheet defines each n-week ROC as 100×(this close / close n−1 weeks earlier)−100. Those four series are later EMA-smoothed and summed with weights 1, 2, 3 and 4; the finished weighted sum appears on only the last two rows and is omitted.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
19 of 46 in the Rate of Change track
19941-2 pp.Next on Rate of ChangeConstructing gold-mining rate-of-change tripwires for Treasury bondsThe gold-mining proxy is a simple arithmetic average of four Thursday gold-mining closes after each close is multiplied by a fixed scaling factor. The four factors are 39.912, 20, 9.3957, and 36.
All readings on this track · 46 readings
  1. 1985Constructing excess and momentum difference-curve oscillators
  2. 1988Five reading rules for smoothed indicator charts
  3. 1989Momentum overlays that speed moving-average oscillators
  4. 1990A laboratory template that constructs Rate of Change as a pane module
  5. 1991Volume-scaled rate of change as a momentum construction
  6. 1991Three-indicator market overview from tape, sentiment and rates
  7. 1991Three-component trend model with rate-of-change filters
  8. 1992A KST oscillator from a weighted rate-of-change stack
  9. 1992Four-window weighted rate-of-change composite
  10. 1992Constructing multi-span smoothed rate-of-change filters
  11. 1992Constructing a four-horizon summed rate of change
  12. 1992Constructing KST from four weighted smoothed rates of change
  13. 1992Constructing a composite from weighted smoothed rates of change
  14. 1992Three-horizon KST maturity alignment
  15. 1992Construct a bond-led dividend-to-bond-yield regime first
  16. 1992Constructing relative-strength KST from weighted rate-of-change
  17. 1993Constructing a volume oscillator from average ratios and smoothed rate of change
  18. 1994Gold as a cycle clock for commodities and yields
  19. 1994Constructing a composite from weighted, smoothed rate-of-change windows
  20. 1994Constructing gold-mining rate-of-change tripwires for Treasury bonds
  21. 1994A capacity-stress checklist across commodities, bonds, and breadth
  22. 1994Rate of change parameters for testable entries
  23. 1994Constructing rate-of-change midpoints, lookbacks and divergence
  24. 1994Lead oscillator breaks need price trendline confirmation
  25. 1994Nested averages for an annual momentum curve
  26. 1994Evaluating a Coppock-style rate of change as a bottom-regime filter
  27. 1995A weighted eleven-month Dow rate of change as one testable timing procedure
  28. 1996Named lookbacks, thresholds, and streaks for entry rules
  29. 1997A midpoint rate-of-change test for bond trend follow-through
  30. 1997Constructing a short-rate-adjusted equity momentum filter
  31. 1998Daily momentum rank-churn as a portfolio-construction problem
  32. 1999Constructing a lagged rate of change cycle system
  33. 2000A triple delay line then a one-bar elliptic oscillator
  34. 2001Confirming rate of change divergences with price
  35. 2001Momentum trendline breaks need price confirmation
  36. 2001Market breadth, On-balance volume, and Rate of Change as a combined timing framework
  37. 2001Know Sure Thing with stacked horizons and trendline confirmation
  38. 2003Constructing a mechanical system from a rate of change condition
  39. 2003Constructing momentum from two closes and spotting divergence
  40. 2003Formula choice tilts which momentum mismatches count as divergences
  41. 2004RSI and momentum agreement as an asymmetric filter
  42. 2005Constructing price-normalized moving-slope hybrids
  43. 2005Unsigned speed gates on a fixed average-cross pair
  44. 2007Rebuilding rate of change as a path-weighted oscillator
  45. 2008Construct Special K so short-horizon signals stay inside the primary trend
  46. 2013Restore volume balance before adding another price-time indicator
By fieldIndicators and filters682 readingsBy year199483 readings
All 50 readings tagged Rate of Change
Also on Rate of Change5 readings
1992Constructing a four-horizon summed rate of change1992Constructing KST from four weighted smoothed rates of change1992Constructing a composite from weighted smoothed rates of change1992Constructing relative-strength KST from weighted rate-of-change1994Nested averages for an annual momentum curve