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1984issue C041-19

How to construct a maximum-entropy cycle model

A maximum-entropy fit can resolve dominant cycles from a relatively short ordered series, and the same coefficients can later produce a forecast consistent with those cycles. Construction starts with lookback and sample interval, a decision on data differencing, and order selection by final prediction error. Spectral analysis then turns those coefficients into power or amplitude so the peaks can be checked.

  • Start with sixty to one hundred twenty observations, and prefer a series that covers at least the longest cycle of interest.
  • Skip data differencing unless the goal is a momentum-style forecast or the optimizer flags it.
  • In automatic mode, search order and sample interval with final prediction error, then keep the last-pass order if that rerun at the stored optimum is smaller.
  • Treat a single broad peak at order one or two, an error minimum at the largest allowed order, or several local minima as a reason to revise the window, sample interval, or differencing choice.
Entries in this reading3 entries
Spectral analysis24 readingsCurrent trackMaximum entropy spectrum analysis30 readingsDominant cycle detection119 readings

What the fit produces

A maximum-entropy spectrum is a high-resolution spectrum estimated from a short ordered series by fitting coefficients that can later drive a cycle-consistent forecast. The same coefficients that resolve dominant cycles can later produce a forecast consistent with those cycles.

Spectral analysis converts those fitted coefficients into power or amplitude versus frequency or cycle length so peaks can be compared and the model checked. The dominant cycle is the strongest periodic component identified in the fitted spectrum, and it is used to judge whether the selected order and sample interval resolved a usable cycle.

Choose lookback and sample interval

Sixty to one hundred twenty observations are a practical starting lookback, and the series should ideally cover at least the longest cycle of interest.

The sample interval is the smoothing-and-resampling stride applied before the fit. Changing the sample interval shortens the plotted frequency range by the reciprocal of that interval and can move peak locations, so spectra from different intervals are not directly overlaid.

Decide whether to difference

Data differencing replaces each observation with its change from the prior bar to weaken a long trend when momentum, not level, is the intended input. Differencing is mainly for momentum-style forecasts and should be skipped unless that is the goal or the optimizer flags it.

Pick order with final prediction error

Automatic mode searches order and sample interval with a final-prediction-error criterion, while manual mode lets the user set coefficient length and the moving-average resample stride. Final prediction error is the order-selection score computed at each fit iteration, and the minimizing order is the recommended model length.

In automatic mode the fit is repeated for sample intervals one through five, then rerun at the stored optimum. If the last pass picks a smaller order, that last-pass order is the one recommended for spectrum work and forecasting.

Final prediction error by MEM order

The auto MEM search settles on sample interval 2 and order 15, where final prediction error bottoms. The primary series is the last printer plot in Figure 1, run with M fixed at that order; the reference series is the earlier D=2 pass that first located the same minimum. Use the plus-marked order as the coefficient length to carry into the spectrum and the forecast.
The auto MEM search settles on sample interval 2 and order 15, where final prediction error bottoms. The primary series is the last printer plot in Figure 1, run with M fixed at that order; the reference series is the earlier D=2 pass that first located the same minimum. Use the plus-marked order as the coefficient length to carry into the spectrum and the forecast.

Auto mode scanned sample intervals D=1 through 5. Each printer plot marks the FPE minimum with a plus. The last pass used the optimized order M=15 rather than the longest order tried on the first D=2 pass.

Convert coefficients into a spectrum

Spectrum output may use log power from 0 to -40 dB or linear amplitude, with frequency in cycles per day preferred over cycle length. Values between -20 and -40 dB are only marginally significant.

Revise a bad window

A minimizing order of one or two yields a single broad peak and usually means a bad window, too large a sample interval, or a strong trend in noisy data, so the lookback or differencing choice should be revised.

If the error minimum sits at the largest allowed order or the error curve has several local minima, the series is too short or too little smoothing was applied. Lengthen the window toward at least three times sample interval times order when possible.

What remains after the plot

Fitted coefficients are stored with the spectrum values and remain available after the plot. The implementation is a computational subroutine that expects a user-supplied price-volume matrix rather than its own data feed or graphics.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
2 of 28 in the Maximum entropy spectrum analysis track
19841-16 pp.Next on Maximum entropy spectrum analysisConstructing a maximum-entropy forecast from a chosen lookbackCoefficient count and size are estimated from the chosen data-length alone, and that window is treated as the whole process being extrapolated.
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 year198412 readings
All 30 readings tagged Maximum entropy spectrum analysis
Also on Maximum entropy spectrum analysis5 readings
1987Assembling short-lookback maximum-entropy cycle forecastsSpectral analysis1989Evaluating commodity cycle personalities with spectral histogramsSpectral analysis1990Year-over-year dominant cycle personality auditSpectral analysis1992Stationarity states on synchronized futures spectral contoursSpectral analysis1997A spectral estimator that retunes indicators to the measured cycleSpectral analysis