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1997issue C111-5

A spectral estimator that retunes indicators to the measured cycle

A measured dominant cycle can be treated as a live length parameter for indicators. The archive builds that measurement with a maximum-entropy estimator so the window can follow one cycle, rather than stretching a Fourier transform until the cycle is assumed to stay put.

  • A measured cycle period is treated as an independent construction parameter so indicator lengths can be retuned to current conditions instead of remaining on fixed settings.
  • Fourier analysis of a windowed price series is constrained to stationarity inside the window and to integer numbers of cycles, which leaves multi-day gaps among identifiable periods in a 64-day daily window.
  • The maximum-entropy estimator compares the windowed series with a noise-driven tunable filter and can set data length dynamically to one dominant cycle.
  • The same measurement also separates a cycle mode from a trend mode, because a cycle-only overlay is described as applicable only about 15 percent of the time.
Entries in this reading3 entries
Spectral analysis24 readingsCurrent trackMaximum entropy spectrum analysis30 readingsDominant cycle detection119 readings

A cycle period as a construction parameter

Indicator length is often left on a fixed setting. In this construction a measured cycle period is treated as an independent parameter, so those lengths can be retuned to current conditions.

The archive workflow is a lesson in how that measurement is built. Editorial comments below are labelled as such and are not part of the source.

Limits of a windowed Fourier spectrum

Fourier spectral analysis of a windowed price series is constrained in two ways. The series must be treated as stationary inside the window, and only integer numbers of cycles are identifiable. In a 64-day daily window those rules leave multi-day gaps among the periods that can be identified.

Lengthening the same construction to 256 daily observations can tighten period resolution near a 16-day cycle to about one day. That tighter grid still requires the cycle to remain consistent across the entire longer window.

Reading amplitude against period

A spectrum display plots amplitude against cycle period on a logarithmic decibel scale so cyclic components can be compared visually. Each 3 dB drop halves power, and a 20 dB span covers a 100-to-1 amplitude range.

On a theoretical 24-bar cycle, and on a March 1996 Treasury bond series, Fourier energy is spread across a wide band of periods. The intended cycle cannot be isolated from that transform.

Building the maximum-entropy estimator

Maximum entropy spectrum analysis is built as a comparison, not as a longer transform. The construction compares the windowed series with the output of a noise-driven tunable filter, then sweeps the filter's transfer response to recover the frequency content of the data.

Because that estimator is not bound by Fourier windowing or by integer-cycle rules, the data length can be set dynamically to one dominant cycle. Dominant cycle detection from the prior day sizes the current window.

MESA lock on a constructed 24-bar sinewave

A constructed 24-bar wave oscillates between about 33.5 and 46.5 from January through May 1994. On 1 June 1994 the MESA96 panel reads close 38.42 and a 23-bar dominant cycle, and the red trace is the software’s forward sine rather than a runaway projection. Swing highs, swing lows and the last bar were read from the sinewave.ttd screen; the last close and cycle length are the readout values.
A constructed 24-bar wave oscillates between about 33.5 and 46.5 from January through May 1994. On 1 June 1994 the MESA96 panel reads close 38.42 and a 23-bar dominant cycle, and the red trace is the software’s forward sine rather than a runaway projection. Swing highs, swing lows and the last bar were read from the sinewave.ttd screen; the last close and cycle length are the readout values.sinewave.ttd · Daily · 1994-01-01T00:00:00.000Z to 1994-06-30T00:00:00.000Z

File sinewave.ttd is a constructed 24-bar cycle. Price path is digitized from the screenshot (vertical ticks are two points, so readings are to the nearest half point) except the last close 38.42, cycle 23 and phase 2.465, which are the software readout. The forward sine is only the short red arc drawn into June, not an extrapolated full cycle.

The same measurement for cycle and trend

The same cycle measurement is also used to separate a cycle mode from a trend mode. A cycle-only overlay is described as applicable only about 15 percent of the time, so the construction needs a trend-mode counterpart.

The source concludes that cycle-finder averaging and Fourier transforms lack the resolution and agility needed for dynamic indicator construction, while a high-resolution maximum-entropy estimate supplies both.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
17 of 28 in the Maximum entropy spectrum analysis track
20001-7 pp.Next on Maximum entropy spectrum analysisConstructing a Hilbert dominant cycle and a maximum-entropy refinementA uniformly weighted average plotted at the right edge lags by half the window width, and a linearly weighted average lags by one-third of that width, so observation-window-lag is an explicit design knob.
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 year199756 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 analysis1992Stationarity states on synchronized futures spectral contoursSpectral analysis