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2005issue C091-4

Constructing price-normalized moving-slope hybrids

A rate of change already divides lookback change by price so differently priced series share a scale. Replacing the two-point difference with a rolling least-squares slope, then dividing by a lagged price, keeps that scale-free property while the construction itself chooses smoothness versus timeliness.

  • A rate-of-change series is lookback change divided by price, which removes the level bias that appears when two differently priced indexes are compared on raw change.
  • A moving slope is the slope of a least-squares line fitted over a chosen lookback and rolled forward one observation at a time; a two-period moving slope equals a one-period change, and that identity rarely holds once the lookback is longer.
  • MSROC divides the slope over N plus one observations by the price N periods earlier, so the same scale-free series can rank members, form an equal-weight group slope, or size a pair.
  • A moving correlation of two MSROC series can mark intervals when typically aligned series temporarily decouple, and the same construction can be applied to a non-price input such as the monetary base.
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Current trackRate of Change50 readingsLinear regression112 readingsMoving average449 readings

A scale-free two-point change

A rate-of-change series is the lookback change divided by price. That division removes the level bias that appears when two differently priced indexes are compared on raw change. The numerator is still a two-point difference. The rest of the construction is about what replaces that difference, and how the result stays comparable across series.

Replace the difference with a moving slope

A moving slope is the slope of a least-squares line fitted over a chosen lookback and then rolled forward one observation at a time. Linear regression supplies the line. The slope is the line’s vertical change over the window divided by the horizontal span. The moving-average idea supplies the roll: a one-shot statistic becomes a continuous series.

A two-period moving slope equals a one-period change. That identity is described as rarely holding once the lookback is longer. On a 25-day window, a moving-slope series of the S&P 500 was presented as smoother than both the matching rate of change and a 25-day Wilder RSI shown for comparison. From 1993 through early 2005, the 25-day rate of change of the S&P 500 reversed direction 1,493 times, while the 25-day moving slope reversed 492 times, with turns described as equally timely.

Moving slopes of daily lows reached larger extremes than moving slopes of daily highs at both peaks and valleys. That pattern was presented as corresponding to narrower daily ranges at tops and wider daily ranges at bottoms.

S&P 500 25-day moving slopes of highs and lows

The 25-day least-squares slope of S&P 500 lows runs farther than the slope of the highs at every swing in this May 2004–February 2005 window, which is how the article shows daily ranges tightening into tops and stretching into bottoms. Levels were read from the published plot; the source prints no table of these series.
The 25-day least-squares slope of S&P 500 lows runs farther than the slope of the highs at every swing in this May 2004–February 2005 window, which is how the article shows daily ranges tightening into tops and stretching into bottoms. Levels were read from the published plot; the source prints no table of these series.S&P 500 · 25-day · 2004-05-01T00:00:00.000Z to 2005-02-28T00:00:00.000Z

Lookback is the article’s 25-day regression on daily highs versus daily lows. Values are digitized from the raster to the nearest 0.1 slope unit, so peaks and troughs are approximate.

Divide by a lagged price

The moving-slope rate of change, or MSROC, is the moving slope over N plus one observations divided by the price N periods earlier. That lagged divisor makes the slope measure independent of price level. The hybrid keeps the rate-of-change purpose of a common scale, and it does so without sending the slope through a second smoother.

Rank a group, size a pair, or leave price

Group means of that price-independent series create an equally weighted sector slope. That is the moving-average operator applied across members of a group, not only across time.

A pair identity sets PriceA times QuantityA times MSROCA equal to PriceB times QuantityB times MSROCB. The same scale-free series can therefore size a pair.

A moving correlation of two MSROC series, illustrated with 20-day MSROCs and a 10-day correlation window, is used to mark intervals when typically aligned series temporarily decouple. Raw rate-of-change series were described as too jagged for the same profile.

The same MSROC construction can be applied to a fundamental series such as the monetary base by comparing a shorter-window MSROC with a longer-window MSROC and a stated policy target.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
42 of 46 in the Rate of Change track
20051-3 pp.Next on Rate of ChangeUnsigned speed gates on a fixed average-cross pairUnsigned speed is the absolute close-to-close change on a bar, so an advance and a same-size decline share one magnitude.
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 year2005104 readings
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Also on Rate of Change5 readings
1985Constructing excess and momentum difference-curve oscillators1988Five reading rules for smoothed indicator charts1989Momentum overlays that speed moving-average oscillators1990A laboratory template that constructs Rate of Change as a pane module1992Constructing a four-horizon summed rate of change