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1992issue C041-10

Stationarity states on synchronized futures spectral contours

This article teaches a three-state reading of a price-aligned spectral contour so a cycle length is used as a timing reference only while the estimate stays stationary.

  • Year-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.
  • Stacking each day's spectrum as a contour under the matching price bar makes persistence, simultaneous periods, cyclic dropout, and the placement of superimposed cyclic extremes visible in calendar time.
  • When period changes abruptly, cycle analysis is invalid for about half a cycle at each transition because the lookback mixes nonstationary data.
  • Energy present at all measured periods was treated as noise, and no cycle-based inference was drawn from that stretch.
Entries in this reading3 entries
Spectral analysis24 readingsCurrent trackMaximum entropy spectrum analysis30 readingsDominant cycle detection119 readings

What a spectral contour shows

Spectral analysis decomposes ordered market observations into cycle-length components whose strength can be tracked from bar to bar. Stacking each day's spectrum as a contour under the matching price bar makes persistence, simultaneous periods, cyclic dropout, and the placement of superimposed cyclic extremes visible in calendar time. That calendar-aligned map of relative period strength is the spectral contour.

A short-record filter bank

Maximum entropy spectrum analysis is treated as a bank of filters spanning periods from eight to 50 days, with component amplitudes compared on a decibel scale relative to the strongest component. The maximum entropy spectrum is a short-record spectral estimate formed by comparing the relative strength of period-tuned filters across a fixed lookback. The dominant cycle is the period that currently holds the largest relative amplitude in the measured band. The filter bank is that set of period-tuned filters spanning the defined range of cycle lengths.

When the estimate is not valid

Stationarity is stability of cycle content across the analysis window. Without it a period estimate is not valid. When period changes abruptly, cycle analysis is invalid for about half a cycle at each transition because the lookback mixes nonstationary data. A short-record entropy estimate is contrasted with a longer-record Fourier transform that market series seldom keep stationary enough to support.

Treasury-bond and equity-index cases

In the December Treasury-bond case, a dominant period near 20 days ended on 28 June 1991 and was replaced by an eight- to 12-day band together with energy longer than 50 days. Editorial note: that handoff is a break in stationarity, after which the contour holds two concurrent ridges rather than one persistent length.

In the December equity-index case, the stronger period wandered between 16 and 30 days, and a late stretch of about 13 days showed energy at all measured periods, which was treated as noise with no cycle-based inference. Editorial note: a wandering dominant period is already a stationarity problem, and the late stretch is broadband noise.

Metals, meats, currencies, and grains

Gold, live cattle, and live hogs were shown with little stable structure below 50 days, the two meat contracts dominated by broadband spectral fill. Editorial note: those meat contours stay in the broadband-noise state, so no short-band dominant cycle is treated as a timing reference.

Two currency contracts did not share the same August structure: one showed a brief 15-day ridge, the other a fairly consistent 12-day ridge under a trend. Cocoa concentrated near 12 to 14 days from April through July and then roughly doubled after the trend turned up, while wheat showed a relatively strong 12-day component over the last four months of an uptrend. Editorial note: cycle personality is contract-specific, and cocoa's later doubling is a period change that leaves the earlier length invalid across the transition.

December 1991 cocoa: 12–14 day cycle, then a doubled noisy length

Cocoa futures (December 1991) show a fairly regular 12-to-14-day swing while prices fall from April into July, then roughly double that length once the trend turns up and the spectral ridge gets noisy. Cycle-length labels (12, 14, 26) are those printed on the source chart. Price points were read from the plotted bars, not copied from the page art.
Cocoa futures (December 1991) show a fairly regular 12-to-14-day swing while prices fall from April into July, then roughly double that length once the trend turns up and the spectral ridge gets noisy. Cycle-length labels (12, 14, 26) are those printed on the source chart. Price points were read from the plotted bars, not copied from the page art.Cocoa December 1991 futures · daily · 1991-04-01T00:00:00.000Z to 1991-12-20T00:00:00.000Z

MESA filter bank 8–50 days; December cocoa through the 20 Dec 1991 quote. Cycle lengths are the source annotations, not a second digitized series. Prices are approximate readings from a coarse raster (~20-point grid); do not treat them as ticks.

How often the structure appears

Year-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. Cycle personality is a contract's tendency, when cyclic at all, to concentrate energy in a recurring period band.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
14 of 28 in the Maximum entropy spectrum analysis track
19971-3 pp.Next on Maximum entropy spectrum analysisHidden horizon assumptions in dominant-cycle readingsA power-spectrum peak names a dominant-cycle only after analysis-span, bar size, and dynamic-range have already been chosen.
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 year1992115 readings
All 30 readings tagged Maximum entropy spectrum analysis
Also on Maximum entropy spectrum analysis5 readings
1984How to construct a maximum-entropy cycle modelSpectral analysis1987Assembling short-lookback maximum-entropy cycle forecastsSpectral analysis1989Evaluating commodity cycle personalities with spectral histogramsSpectral analysis1990Year-over-year dominant cycle personality auditSpectral analysis1997A spectral estimator that retunes indicators to the measured cycleSpectral analysis