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2000issue C071-6

A triple delay line then a one-bar elliptic oscillator

Subtracting price N bars ago from current price leaves a zero-mean residual, but a single rate-of-change still makes residual height depend on cycle length. Differencing a filtered series at six and twelve bars evens those amplitudes; an elliptic smoother under a one-bar lag cap, then a second smooth, makes the oscillator a two-line cross.

  • A rate-of-change subtracts price N bars ago from current price so components that stay nearly constant cancel, leaving a zero-mean residual instead of a trending price level.
  • A six-bar rate-of-change only partly removes longer cycles and also cancels harmonics of six bars; shortening to four bars passes more short-cycle energy but is weaker at removing trend.
  • A triple delay-line canceller that differences a filtered series at six and twelve bars produces residuals whose cycle amplitudes are nearly uniform.
  • After the detrend, an elliptic smoother under a one-bar lag cap is applied, then that output is smoothed once more, and crossings of the two lines are the read events.
Entries in this reading2 entries
Detrended Price Oscillator3 readingsCurrent trackRate of Change50 readings

Cancel near-constant components first

Subtracting price N bars ago from current price cancels components that stay nearly constant over that interval, leaving a zero-mean residual instead of a trending price level. That N-bar difference is the rate-of-change used as the first canceling stage.

A single lookback leaves uneven residual height

A six-bar rate-of-change only partly removes cycles much longer than six bars and also cancels harmonics of six bars, so residual amplitude varies by cycle length.

A shorter window does not even the heights

Shortening the lookback to four bars passes more short-cycle energy but is weaker at removing trend. Longer-cycle residual height falls to about plus or minus 2 versus about plus or minus 4 at six bars.

Finish cancellation with a triple delay line

A triple delay-line canceller that differences a filtered series at six and twelve bars produces residuals whose cycle amplitudes are nearly uniform across the periods of interest.

Feed the detrend the midpoint price

The price input to the detrend is the midpoint of each bar's high and low. That midpoint price is the input series so the detrend and the elliptic smoothing filter see the bar body rather than a single print.

Spend the one-bar lag budget on elliptic smoothing

After the detrend, an elliptic smoother is designed under a one-bar lag cap, with out-of-band attenuation set to -20 dB and a notch at 0.5 cycles per day, a two-bar period. Substituting a one-bar momentum prediction, twice current price minus the prior price, for raw price in the elliptic filter is used to offset remaining lag.

Read crossings of two smoothed lines

The oscillator is built by sending the detrend into the elliptic smoother and then smoothing that output once more. Crossings of the two smoothed lines are the read events. Under trend-mode caution, those crossings are less trustworthy when price is in a persistent trend than when it is cycling, because residual long-cycle energy still leaks through. The detrend is also framed as a first stage for later Hilbert-transform and polynomial-predictive filters.

Two-line elliptic detrend, daily prices into March 1996

A trader should treat the fast residual crossing the slower elliptic smooth as the cyclic turn, not a wait for a zero test. After the late-February washout the fast line is already back at +0.96 while the slow line is still at −2. Last readings 0.96 and −2.00 plus the drawn zero line set the vertical scale; the rest of each curve was digitized from that TradeStation plot.
A trader should treat the fast residual crossing the slower elliptic smooth as the cyclic turn, not a wait for a zero test. After the late-February washout the fast line is already back at +0.96 while the slow line is still at −2. Last readings 0.96 and −2.00 plus the drawn zero line set the vertical scale; the rest of each curve was digitized from that TradeStation plot.Daily · 1995-08-28T00:00:00.000Z to 1996-03-01T00:00:00.000Z

Y-scale inferred from the quoted finishes (0.96 and −2.00) against the zero line; interior points are approximate to about 0.3 oscillator units because the screenshot prints no y-axis. Daily bars, late August 1995 through 1 March 1996.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
33 of 46 in the Rate of Change track
20011-4 pp.Next on Rate of ChangeConfirming rate of change divergences with priceSize the rate-of-change window and the spacing of disagreements to the swing under study.
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
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2014Construct a trough-to-trough cycle map with the Detrended Price OscillatorDetrended Price Oscillator2014Dual detrended oscillators and dual Bollinger Band channelsDetrended Price Oscillator1985Constructing excess and momentum difference-curve oscillators1988Five reading rules for smoothed indicator charts1989Momentum overlays that speed moving-average oscillators