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1992issue C091

Constructing KST from four weighted smoothed rates of change

KST is assembled in three sequential stages: four rate-of-change series, an independent moving average on each series, and a weighted sum of the four smoothed results. Construction tables give short-, intermediate-, and long-horizon parameter sets for daily, weekly, or monthly bars, including a short-term weekly exponential specification.

  • Assemble the composite in three stages: compute four rate-of-change series, smooth each series with its own moving average, then form a weighted sum.
  • Form each rate-of-change from the current close divided by the close n periods earlier, multiply by 100, then reduce by 100 so an unchanged price is centered on zero.
  • Smooth with a simple moving average or an exponential moving average; an E mark selects the exponential update, whose smoothing-constant is 2 divided by n plus 1.
  • Choose among short-, intermediate-, and long-horizon tables for daily, weekly, or monthly bars, including the short-term weekly exponential set with rate-of-change lengths 3, 4, 6 and 10, smoothing lengths 3, 4, 6 and 8, and weights 1, 2, 3 and 4.
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Current trackRate of Change50 readingsExponential smoothing117 readingsMoving average449 readings

Three sequential stages

KST is a multi-horizon momentum composite built from four smoothed, weighted rates of change rather than from a single lookback. The indicator is assembled in three sequential stages: compute four rate-of-change series, smooth each series with a moving average, then form a weighted sum of those four smoothed series.

How each rate-of-change is formed

A rate-of-change is a close-to-close momentum ratio over a stated lookback, scaled so a zero reading marks an unchanged price over that window. Each 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.

Four weekly ROC windows on the short-term KST sample

The four rate-of-change windows on weekly S&P 500 closes that later receive their own EMAs and weights 1, 2, 3, and 4. A trader can see how the 3-, 4-, 6-, and 10-week legs share a zero center but turn at different speeds. Every point is taken from the short-term weekly KST spreadsheet in Sidebar Figure 2, not traced from a plotted curve.
The four rate-of-change windows on weekly S&P 500 closes that later receive their own EMAs and weights 1, 2, 3, and 4. A trader can see how the 3-, 4-, 6-, and 10-week legs share a zero center but turn at different speeds. Every point is taken from the short-term weekly KST spreadsheet in Sidebar Figure 2, not traced from a plotted curve.S&P 500 · weekly · 1992-01-17T00:00:00.000Z to 1992-05-08T00:00:00.000Z

ROC is ((this week's close / close n weeks earlier) × 100) − 100, so the scale is percent and centered on zero. The printed weighted KST sum appears only on the last two rows, so the chart shows the four unsmoothed ROC inputs rather than the finished oscillator.

Smoothing each series independently

A moving average is a smoother applied independently to each rate-of-change series before the weighted combination, either as a simple window or as an exponential update. Each rate-of-change series may be smoothed with either a simple moving average or an exponential moving average. An E mark in the parameter table designates the exponential choice.

Exponential smoothing is a recursive average that blends the newest observation with the prior average using a constant equal to 2 divided by the lookback plus one. The smoothing-constant is the alpha used in the exponential update; it shrinks as the stated lookback lengthens. For a three-period lookback that constant equals 0.50. The first exponential average is seeded with the first available observation, and recursive updating begins on the following period.

Horizon tables and bar length

Construction tables supply separate short-, intermediate-, and long-horizon parameter sets, with variants that consume daily, weekly, or monthly bars. The short-term weekly exponential specification uses rate-of-change lengths 3, 4, 6 and 10, exponential-smoothing lengths 3, 4, 6 and 8, and weights 1, 2, 3 and 4.

The weekly weighted sum

In the worked weekly example the four exponential constants are 0.50, 0.4, 0.29 and 0.22, and the composite equals the first smoothed series plus two, three and four times the remaining three smoothed series. The weighted-sum is the last construction step, in which each independently smoothed rate-of-change is multiplied by a preset weight and the four products are added.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
12 of 46 in the Rate of Change track
19921-1 pp.Next on Rate of ChangeConstructing a composite from weighted smoothed rates of changeThe 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.
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 a composite from 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