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1992issue C091-7

Constructing a four-horizon summed rate of change

Market swings can be treated as overlapping cycles. This archive walk-through rebuilds four smoothed rate-of-change series, applies span-weighting so the longer lookbacks dominate, and reads the summed rate of change through nested confirmation plus a price-structure check.

  • Several smoothed rate-of-change series can reverse together at major turns and stay in conflict during trading ranges, which is the reason for stacking more than one lookback.
  • Span-weighting assigns larger multipliers to longer lookbacks so the primary cycle still dominates the stack while shorter components can pull the turn forward of a single slow rate of change.
  • Nested confirmation reads the composite in three layers: a direction change in the summed line, a cross of that line through its moving average, and a reversal of the moving average itself.
  • The same four-horizon stack can be rebuilt on daily or weekly bars, and the published lookbacks, smoothers, and weights are a starting specification rather than a unique optimum.
Entries in this reading3 entries
Current trackRate of Change50 readingsExponential smoothing117 readingsMoving average449 readings

Overlapping cycles and a late clock

Market swings are framed as overlapping time cycles. Several smoothed rate-of-change series can therefore reverse together at major turns and remain in conflict during trading ranges.

A nine-month moving average of a 24-month rate of change is presented as tracking primary bull and bear swings. That single slow series remains slow to reverse and is therefore late at some turns, including the late-1989 episode on the illustrated equity benchmark.

Smoothed S&P rates of change, three lookbacks

A trader should see the nine-month average of 24-month rate of change still easing in late 1989 while the two faster oscillators have already turned up — that lag is the late clock a single slow ROC sets. The points were read from the three oscillator panes of the printed Figure 1 chart, so turning-point heights are approximate rather than table-exact.
A trader should see the nine-month average of 24-month rate of change still easing in late 1989 while the two faster oscillators have already turned up — that lag is the late clock a single slow ROC sets. The points were read from the three oscillator panes of the printed Figure 1 chart, so turning-point heights are approximate rather than table-exact.S&P Composite · Monthly · 1978-01-01T00:00:00.000Z to 1990-12-31T00:00:00.000Z

Each pane is a moving average of a rate of change, not raw ROC. The 24-month series only appears around 1980 after the lookback plus the nine-month smooth. A scanned line chart cannot recover monthly prints.

Span-weighting four lookbacks

The stated construction stacks four smoothed rate-of-change series and weights each roughly in proportion to its lookback. The aim is for longer-term momentum to change direction sooner than a single slow rate of change while still limiting short-lived flips.

Span-weighting is the construction rule that assigns larger multipliers to longer lookbacks so the primary cycle still dominates the stack while shorter components can pull the turn forward.

One long-horizon recipe uses 9-, 12-, 18-, and 24-month rates of change. It applies a six-month moving average to the first three series and a nine-month moving average to the 24-month series, then assigns weights of 1, 2, 3, and 4 before summing. The finished object is a summed rate of change: four separate series, each smoothed, each multiplied by its span-based weight, then added.

How the composite is calculated

A rate of change is a centered momentum reading formed by dividing the latest close by the close n periods earlier, multiplying by 100, and subtracting 100 so zero is the balance point.

Calculation is specified in three steps. First, form each rate of change as the latest close divided by the close n periods earlier, times 100, minus 100. Second, smooth each series with a simple or exponential moving average. Third, multiply by the assigned weight and add the four terms.

The moving average in that second step is a simple or exponential smoother applied to each rate-of-change series before it is weighted. Exponential smoothing is a recursive average that updates with a constant of 2/(n+1), blending the newest observation into the prior average. The first bar is seeded from the first available value.

Sampling on monthly, weekly, and daily bars

Suggested parameter sets are supplied for daily, weekly, and monthly sampling. The same four-horizon stack can be rebuilt on daily or weekly bars for shorter swings.

One short-term weekly stack uses 3-, 4-, 6-, and 10-week rates of change, smoothed with exponential averages of 3, 4, 6, and 8 weeks, and weights 1 through 4.

Nested confirmation and price structure

Three nested confirmation layers are defined for the composite: a direction change in the summed series, a cross of that series through its moving average, and a reversal of the moving average itself. That second moving average is applied to the finished composite as a signal line.

The stack is described as a filter that should be checked against other indicators and a price-structure confirmation such as a moving-average cross or trendline break.

Oscillator tools used on other momentum series are treated as applicable to the summed line. Those tools include divergences, stretched readings, trendline breaks, and chart patterns. A joint trendline break on the indicator and on price is highlighted as extra confirmation of a moving-average cross.

Limits of the published specification

Prolonged one-way trends can generate premature reversal readings. Abrupt policy or news shocks can pass the slow composite with little immediate response.

The published lookbacks, smoothers, and weights are offered as a starting specification rather than a unique optimum.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
11 of 46 in the Rate of Change track
19921-1 pp.Next on Rate of ChangeConstructing KST from four weighted smoothed rates of changeAssemble the composite in three stages: compute four rate-of-change series, smooth each series with its own moving average, then form a weighted sum.
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 KST from four weighted smoothed rates 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