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1991issue C021-3

Half-cycle average plot shift versus cycle attenuation

A half-cycle moving average can be taught as a two-part construction bench on a sine-wave price model locked to a known dominant cycle. Isolate end-point plotting lag first, isolate amplitude attenuation second, and only then ask whether those geometric effects can be recombined on unordered market prices.

  • A half-cycle moving average is described as typically riding the highs of falling stretches and the lows of rising stretches in the financial series examined.
  • The conventional plot places the average at the latest period. On a 90-period sine wave, a 45-period centered plot tracks the wave, while the same window at the end of the interval does not sit on that path.
  • Amplitude loss from averaging is not constant. Illustrated averages of a +1 and -1 sine wave peaked and troughed at 0.62, and the difference versus the price line varied from about +0.4 to -0.4.
  • Combining the upward shift-effect from rightward plotting with the downward offset from attenuation is difficult on actual prices, which lack sine-wave geometry and a precisely known cycle phase.
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Sine-wave price model2 readingsCurrent trackDominant cycle detection119 readingsMoving average449 readings

A construction bench on a known cycle

Editorial: TradersWeek presents the half-cycle moving-average as a two-part construction bench on a sine-wave-price-model locked to a known dominant-cycle. Isolate the lag of an end-point-plot first, isolate amplitude attenuation second, and only then ask whether those geometric effects can be recombined on unordered market prices.

In the financial series examined, a half-cycle moving-average is described as typically riding the highs of falling stretches and the lows of rising stretches.

End-point plot and the shift-effect

The conventional chart plot places a moving-average at the latest period rather than at the center of the window that generated it. A centered-plot draws the average at the midpoint of the bars that produced it. An end-point-plot draws the same average at the latest bar, which shifts it forward in time.

On a 90-period sine wave, a 45-period centered-plot tracks the wave, while the same half-cycle-window plotted at the end of the interval does not sit on that path.

Shifting a centered-plot one period to the right creates a vertical gap versus price. For a one-period horizontal offset the gap height of that shift-effect is treated as a function of drawing scale, with the illustrative relation A = (B2 - 1) when C = 1.

On one illustrated scale where one day occupies about one millimeter and one millimeter equals 4 ticks, a one-day rightward shift is treated as about 4 ticks of positive vertical displacement per day.

Attenuation of the averaged wave

Averaging a sine-wave-price-model whose peaks are +1 and -1 produced illustrated averages that peaked and troughed at 0.62.

Attenuation from averaging is not constant. The plotted difference between a centered-plot and the price line varies from about +0.4 to -0.4.

Recombination on unordered prices

Combining the upward offset from rightward plotting with the downward offset from attenuation is difficult on actual prices, which lack sine-wave geometry and a precisely known cycle phase.

An open construction question is whether attenuation from averaging has a concise closed-form that would allow a more exact adjustment of the plotted average.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
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19911-5 pp.Next on Dominant cycle detectionHalf-cycle average contact as an amplitude-ratio testIn an idealized sine-plus-trend path, a half-cycle average equals price at the cycle extrema only when cycle amplitude matches the secular-trend increment over one-quarter of the period.
All readings on this track · 31 readings
  1. 1982Cycle phase windows for chart signal filters
  2. 1987Constructing a cycle-scaled trend oscillator
  3. 1987Constructing a dominant-cycle grid from marked lows
  4. 1988Cycle lead from staggered exponential averages
  5. 1988Auditing the forty-month stock-price cycle
  6. 1989When long-wave dominant cycles cannot be disproved
  7. 1991Half-cycle average plot shift versus cycle attenuation
  8. 1991Half-cycle average contact as an amplitude-ratio test
  9. 1993Building a restoring-pull indicator from cycle frequency and volume
  10. 1995Regime filters for a dominant long wave
  11. 1995A cycle-tuned lead filter from bounded oscillators
  12. 1998Testable cycle rules instead of fear and greed
  13. 1999Nested Euro cycle timing as one checkable procedure
  14. 2002Constructing an instantaneous trendline from a dominant cycle
  15. 2002Half-cycle center of gravity oscillator from moving-average balance
  16. 2004Testing a locked forty-week cycle with a hold-or-sit-out rule
  17. 2005Nested timing bands for dominant-cycle confirmation
  18. 2005Dominant-cycle baselines versus policy-news narratives
  19. 2006Pairing a dominant-cycle horizon with trend and oscillators
  20. 2006A dominant-cycle split into a trend filter and residual Relative Strength Index
  21. 2007Construct a momentum difference from the dominant cycle
  22. 2007Naive dominant-cycle rules fail without crowd tests
  23. 2012Constructing a dominant-cycle forecast as a timing window
  24. 2012Open-parameter construction of dominant-cycle baselines
  25. 2013Using a second-term election to check a predeclared dominant-cycle forecast
  26. 2014Constructing a dominant-cycle forecast baseline
  27. 2014Quotient transform as an early-onset trend filter
  28. 2014Construct a trough-to-trough cycle map with the Detrended Price Oscillator
  29. 2015Dominant-cycle alignment before an earnings catalyst
  30. 2017Causal reverse exponential average for cycle and trend
  31. 2020Constructing a cycle-plus-trend oscillator from a one-wavelength chord
By fieldIndicators and filters682 readingsBy year199198 readings
All 119 readings tagged Dominant cycle detection
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1999How a five-bar sine-weighted average is assembledSine-wave price model1987Constructing a cycle-scaled trend oscillator1988Auditing the forty-month stock-price cycle1988Cycle lead from staggered exponential averages1991Half-cycle average contact as an amplitude-ratio test