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1991issue C071-13

Cyclic entry from a locked dominant-cycle phase

This construction first judges whether price is in cyclic-mode, then holds one dominant-cycle length fixed and finds phase by correlating price with a same-length sine. Short and long rules are taken from that best-fit angle rather than from a joint description of period, amplitude, and phase.

  • Usable trading cycles are described as present only 15% to 30% of the time, so cyclic-mode must be judged from recent history or a spectrum measurement before any entry rule is applied.
  • After one dominant-cycle length is locked, phase-correlation against a same-length sine at successive starting phases keeps the trial with the largest amplitude. Cycle amplitude is not required.
  • A short entry is defined when that best-fit sine sits at 90 degrees, and a long entry when it sits at 270 degrees, with optional lead or lag around those entry-phase points.
  • The supplied search uses 16 steps of 22.5 degrees over one dominant-cycle lookback. Mapping the correlated phase through a sine lookup rebuilds a zero-mean detrended-replica of price.
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Current trackMaximum entropy spectrum analysis30 readingsDominant cycle detection119 readingsRule-based entry174 readings

The construction is intended only when the market is judged to be in cyclic-mode. That judgment comes first, from a check of recent history or from a spectrum measurement.

A maximum-entropy-spectrum is one named way to decide cyclic-mode and to measure the dominant-cycle length that will be held fixed afterward.

Judge cyclic-mode first

Usable trading cycles are described as present only 15% to 30% of the time. Mode detection is the first task.

Lock one dominant-cycle and search phase

Once a dominant-cycle length is known, it stays fixed for one record’s phase search. Phase is found by correlating price with a sine of that same length at successive phase steps and keeping the trial with the largest amplitude.

The procedure does not require cycle amplitude. Period is measured or estimated, and phase comes from the correlation search.

Turn the best-fit angle into entry rules

A short entry is defined at the highest correlation when the sine is at 90 degrees. A long entry is defined when the sine is at 270 degrees. An optional lead or lag may move those entry-phase points earlier or later than the extreme.

What the triangle-wave example shows

A worked triangle-wave example shows zero correlation at 0 and 180 degrees and maximum correlation when the sine sits at 90 degrees on the last bar.

Sine and cosine over one full cycle sum to a zero product, while an in-phase sine correlated with itself sums to π. Only the matching phase of the estimated dominant-cycle is expected to peak.

Rebuild a detrended-replica from phase

Mapping the correlated phase through a sine lookup recreates a zero-mean detrended-replica of price.

Step the search in discrete increments

The supplied search steps phase in 16 increments of 22.5 degrees. It multiplies price by a 2π sine over one dominant-cycle lookback and retains the increment with the largest sum for each record.

More than 16 phase increments can refine resolution at higher compute cost. The write-up also states, without a demonstration, that the correlation has noise immunity.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
13 of 28 in the Maximum entropy spectrum analysis track
19921-10 pp.Next on Maximum entropy spectrum analysisStationarity states on synchronized futures spectral contoursYear-long daily spectral tallies described cyclic structure as present only 15 to 30 percent of the time, with some futures contracts recurring in the same period bands.
All readings on this track · 28 readings
  1. 1984Constructing maximum-entropy spectra for dominant-cycle forecasts
  2. 1984How to construct a maximum-entropy cycle model
  3. 1984Constructing a maximum-entropy forecast from a chosen lookback
  4. 1985Constructing period-locked half-cycle and full-cycle averages
  5. 1986Why Fourier windows limit dominant-cycle resolution
  6. 1987Assembling short-lookback maximum-entropy cycle forecasts
  7. 1988Why a fitted dominant cycle is not a forecast
  8. 1989Evaluating commodity cycle personalities with spectral histograms
  9. 1989Evaluating next-session cycle forecasts with stops
  10. 1989Constructing cycle-aged volatility trailing stops
  11. 1990A channel signal-to-noise gate for dominant-cycle forecasts
  12. 1990Year-over-year dominant cycle personality audit
  13. 1991Cyclic entry from a locked dominant-cycle phase
  14. 1992Stationarity states on synchronized futures spectral contours
  15. 1997Hidden horizon assumptions in dominant-cycle readings
  16. 1997When market cycles are absent more than present
  17. 1997A spectral estimator that retunes indicators to the measured cycle
  18. 2000Constructing a Hilbert dominant cycle and a maximum-entropy refinement
  19. 2000Switch trend and cycle indicators after a half-cycle dwell test
  20. 2000Constructing a dominant-cycle squelch trend filter
  21. 2000Phasor displays for dominant-cycle construction
  22. 2002Low-lag trendline from elliptic and dominant-cycle notches
  23. 2004Spectral peaks are mode diagnostics, not forecasts
  24. 2004Compressive last-stage oscillator construction
  25. 2013Constructing trend failure curves from qualified-trend transitions
  26. 2014Lookback range, a two-lag smoother, and next-bar fills
  27. 2014Constructing a MESA stochastic with roofing and SuperSmoother filters
  28. 2016Constructing spectral heatmaps for dominant market cycles
By fieldCycles and spectral analysis77 readingsBy year199198 readings
All 30 readings tagged Maximum entropy spectrum analysis
Also on Maximum entropy spectrum analysis5 readings
2000Phasor displays for dominant-cycle construction1984How to construct a maximum-entropy cycle model1984Constructing maximum-entropy spectra for dominant-cycle forecasts1985Constructing period-locked half-cycle and full-cycle averages1986Why Fourier windows limit dominant-cycle resolution