Skip to main content
Track Rate of Change
13 / 46
Search the archiveLibrary
Library

1992issue C101

Constructing a composite from weighted smoothed rates of change

The composite is built in three layers. Compute four zero-centered rates of change, smooth each series with a simple or exponential moving average, then multiply by fixed weights and add the products. Horizon sets publish lookbacks, smoothers, and weights for short, intermediate, and long sampling on daily, weekly, or monthly bars.

  • The composite has three layers: four rate-of-change series, a simple or exponential moving average on each series, and a weighted sum of the smoothed series.
  • Rate of change is the current close divided by the close n periods earlier, multiplied by 100, then reduced by 100 so the series is centered on zero.
  • Exponential smoothing uses a constant of two divided by one more than the lookback length, seeds the first observation, and begins updating on the next period.
  • Horizon sets bundle four lookbacks, four smoothers, and weights of 1, 2, 3, and 4 for short, intermediate, or long sampling on daily, weekly, or monthly bars.
Entries in this reading3 entries
Current trackRate of Change50 readingsExponential smoothing117 readingsMoving average449 readings

Three construction layers

The composite is built in three layers: compute four rate-of-change series, smooth each series with a simple or exponential moving average, then multiply the smoothed series by fixed weights and add the products.

Editorial: treat those steps as three separable construction choices. A reader can rebuild or swap the rate-of-change transform, the smoother, or the weight schedule without treating the finished series as a single opaque formula.

A zero-centered rate of change

Rate of change is the current close divided by the close n periods earlier, multiplied by 100, then reduced by 100 so the series is centered on zero.

In this workflow, rate of change is a close-to-close percentage change over a stated lookback, shifted so the series is centered on zero.

Four weekly S&P 500 rates of change that feed the short-term KST

The four zero-centered weekly rates of change that later get smoothed and weighted into the short-term KST. The 3-week series is the noisiest; the 10-week series stays negative through March and only turns up in April. Every point is copied from the sidebar spreadsheet of S&P 500 weekly closes, 3 January through 8 May 1992.
The four zero-centered weekly rates of change that later get smoothed and weighted into the short-term KST. The 3-week series is the noisiest; the 10-week series stays negative through March and only turns up in April. Every point is copied from the sidebar spreadsheet of S&P 500 weekly closes, 3 January through 8 May 1992.S&P 500 · weekly · 1992-01-17T00:00:00.000Z to 1992-05-08T00:00:00.000Z

Short-term weekly KST uses ROC lengths 3, 4, 6 and 10 weeks. The printed weighted sum appears only on 1 May (6.26) and 8 May 1992 (10.71), too few points to plot as the finished composite.

An explicit smoother

A moving average is a simple or exponential smoother applied to each rate-of-change series before the series are combined. Exponential smoothing is a recursive average that blends the newest observation with the prior average using a smoothing constant.

The smoothing constant equals 2 divided by one more than the lookback length. For a three-period lookback that constant is 0.50.

Each new exponential average equals the prior average plus the smoothing constant times the gap between the new observation and the prior average. Because the first period has no prior exponential average, the first observation seeds the series and smoothing begins on the next period.

A weighted sum

The last construction step is a weighted sum: each smoothed rate-of-change is multiplied by a preset weight and the four products are added.

Published horizon sets

A horizon set is a published bundle of four lookbacks, four smoothers, and four weights chosen for short, intermediate, or long sampling. Suggested parameter sets exist for short, intermediate, and long horizons and may be computed on daily, weekly, or monthly sampling.

In the short-term weekly exponential set, the four rate-of-change lengths are 3, 4, 6, and 10, the matching exponential averages are 3, 4, 6, and 8, and the weights applied before the sum are 1, 2, 3, and 4. The worked weekly example applies exponential constants of 0.5, 0.4, 0.29, and 0.22 to those four smoothers, consistent with 2/(n+1) for n of 3, 4, 6, and 8.

The short-term daily set uses rate-of-change lengths 10, 15, 20, and 30, simple averages of 10, 10, 10, and 15, and the same 1-2-3-4 weights.

The long-term weekly exponential set uses rate-of-change lengths 39, 52, 78, and 104, exponential averages of 26, 26, 26, and 39, and weights 1, 2, 3, and 4.

Editorial: the listed sets share weights of 1, 2, 3, and 4, so the rising schedule can stay fixed while the lookbacks and smoothers change with horizon and sampling.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
13 of 46 in the Rate of Change track
19921-6 pp.Next on Rate of ChangeThree-horizon KST maturity alignmentMarket direction is treated as the interaction of many time cycles, and an important turn is framed as several of those cycles changing direction at once.
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 year1992115 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 relative-strength KST from weighted rate-of-change1994Constructing a composite from weighted, smoothed rate-of-change windows1994Nested averages for an annual momentum curve