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1991issue C051-5

Half-cycle average contact as an amplitude-ratio test

A half-cycle average meets price at a swing extreme only under a special amplitude-to-trend ratio. Treat skim-contact as a coincidence test, then attribute any remaining miss to plot-shift, averaging-attenuation, or session-range-scatter before locking a lookback into a rule-based entry.

  • In 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.
  • The same construction keeps the average from crossing to the far side of price near a full-cycle secular-trend increment divided by 4.74, but those ratios are model limits, not market constants.
  • Most average contacts are attributed to session-range-scatter rather than a stable cycle, because persistent cyclical structure is treated as uncommon.
  • Plot-shift, averaging-attenuation, session volatility, and cyclic content jointly control entry location, and choosing length from a full-cycle estimate down toward a half-cycle length is ranked as the primary adjustment before a rule-based entry.
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Current trackDominant cycle detection119 readingsRule-based entry174 readingsMoving average449 readings

Skim-contact is not a general property

A half-cycle average is a simple moving average whose lookback is set to half of a stated dominant-cycle estimate. Skim-contact is a meeting of price and that short average at a trend extreme. The archive treats that meeting as something that can occur only under a special trend-versus-amplitude ratio, not as a general property of the average.

An idealized amplitude-to-trend limit

In an idealized path that adds a linear trend to a sine of period T, a half-cycle average equals price at the cycle extrema only when cycle amplitude equals the secular-trend increment over one-quarter of T.

In that same construction, the amplitude that keeps the half-cycle average from crossing to the far side of price sits near the full-cycle secular-trend increment divided by 4.74.

Lag and averaging-attenuation without trend

With the trend term removed, the half-cycle average of a sine is another sine scaled by the constant 2/π, and the conventionally plotted average lags the wave by a quarter cycle. Averaging-attenuation is that reduction in cycle amplitude, even when the wave remains sinusoidal.

Those exact ratios are framed as limits of a perfect sine-plus-trend model, not as quantities that market prices are expected to hold.

Critical amplitude-to-trend ratio for half-cycle skim contact

On Newcombe's idealized rising wave, price and the half-cycle average meet at every cycle trough when cycle amplitude equals the trend over a quarter cycle (b = a/4). The curves are his closed forms evaluated at the left-hand sample in Figure 1, a = 4 and b = 1. A trader should treat that trough contact as a coincidence test: if live amplitude is not about one-quarter of the trend over a cycle, expecting the average to skim extremes is not justified by the math.
On Newcombe's idealized rising wave, price and the half-cycle average meet at every cycle trough when cycle amplitude equals the trend over a quarter cycle (b = a/4). The curves are his closed forms evaluated at the left-hand sample in Figure 1, a = 4 and b = 1. A trader should treat that trough contact as a coincidence test: if live amplitude is not about one-quarter of the trend over a cycle, expecting the average to skim extremes is not justified by the math.

Contact is exact only for a pure sine plus linear drift. Newcombe warns these numbers should not be read literally in market prices. He also gives a nearby bound, b ≈ a/4.74, where the average stays at or below price.

Session-range-scatter and uncommon cycles

A follow-up note accepts the amplitude-to-trend condition and adds that session-range-scatter around any cycle also decides whether price reaches the average.

Persistent cyclical structure is treated as uncommon, with an estimate of less than 20 percent of the time, so most average contacts are attributed to varying session range rather than a stable cycle.

Plot-shift on a right-aligned average

Moving a centered average of fixed length to a conventional right-aligned plot opens a vertical gap. That gap is plot-shift, and it is further altered by averaging-attenuation.

On one illustrated currency series, a 12-day average leaves a detrended gap that appears to vary with a cycle, while a 6-day half-cycle average narrows the gap and is shown as placing candidate entries closer to price.

Lookback as the primary adjustment

After listing plot-shift, averaging-attenuation, session volatility, and cyclic content as joint controls on entry location, the archive ranks choosing average length, from a full-cycle estimate down toward a half-cycle length, as the primary adjustment. Dominant-cycle length is the working period estimate used to choose a full-cycle lookback and its half-cycle counterpart.

A rule-based entry is then a testable procedure that fires only when price and the chosen average meet under stated trend, cycle, and range conditions.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
8 of 31 in the Dominant cycle detection track
19931-2 pp.Next on Dominant cycle detectionBuilding a restoring-pull indicator from cycle frequency and volumeCycle length is a market-specific input that can change from day to day, so it must be estimated for each session before a restoring-pull value is formed.
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 fieldCycles and spectral analysis77 readingsBy year199198 readings
All 119 readings tagged Dominant cycle detection
Also on Dominant cycle detection5 readings
1991Cyclic entry from a locked dominant-cycle phase1991Quadratic trend, residual oscillator, and a secondary cycle calendar1999Nested Euro cycle timing as one checkable procedure2000Phasor displays for dominant-cycle construction2014Quotient transform as an early-onset trend filter