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2000issue C031-3

Constructing dominant cycle length from Hilbert phase

A Hilbert-style construction starts from the high-low midpoint, recovers phase from the quadrature-to-in-phase ratio, and reads dominant cycle length as the lag where accumulated phase first exceeds 360 degrees.

  • A Hilbert-style construction can start from the high-low midpoint and split that series into an in-phase and quadrature pair using coefficients 0.635 and 0.338.
  • Instantaneous phase comes from the quadrature-to-in-phase ratio, converted to degrees and remapped when the pair changes quadrant so successive readings stay continuous.
  • Dominant cycle length is the lag at which accumulated phase first exceeds 360 degrees; one scanner stops at 21 bars unless the same test is repeated at longer lags.
  • The raw period and a companion signal-to-noise series are each blended with weights 0.25 and 0.75, and an example forecast rule also requires a period above 20, signal-to-noise above 6, and a positive 10-bar slope of close.
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Current trackFourier analysis41 readingsDominant cycle detection180 readings

From midrange price to a Hilbert pair

A Hilbert-style cycle construction can start from the high-low midpoint as the series that is split into orthogonal components. That split is Fourier analysis: spectral decomposition of an ordered price series into orthogonal components that support phase and period measurement.

The two Hilbert filter legs in the supplied construction are parameterized with the coefficients 0.635 and 0.338. The resulting Hilbert pair is the in-phase and quadrature legs produced by a two-coefficient recursive transform of midrange price. In-phase is the cosine-like Hilbert component used as the real part of the instantaneous phasor. Quadrature is the sine-like Hilbert component used as the imaginary part of the instantaneous phasor.

Recovering and unwrapping phase

Instantaneous phase is recovered from the quadrature-to-in-phase ratio, converted to degrees, and remapped when the component pair changes quadrant. That remapping is a phase unwrap: a quadrant correction that keeps successive phase readings continuous across the 0/360 boundary.

Counting one full rotation

Dominant cycle length is read as the lag at which accumulated phase increment first exceeds 360 degrees. That bar count is the dominant cycle: the lag at which accumulated phase change first completes a full 360-degree rotation.

One supplied period scanner only tests lags through 21 bars. A longer maximum requires repeating the same 360-degree accumulation test at additional lags.

Blending the raw period count

The raw period count is recursively blended with weight 0.25 on the new count and 0.75 on the prior smoothed period. That step is the period-smooth, a recursive blend that mixes a newly counted cycle length with the prior smoothed period.

Gating the reading with signal-to-noise

A companion signal-to-noise series compares Hilbert amplitude with recent range and applies the same 0.25/0.75 recursive blend. Signal-to-noise is a constructed reliability score that compares Hilbert amplitude with recent high-low range.

Reusable measures and an example forecast rule

The finished cycle-period and signal-to-noise measures are built as reusable indicators that can be placed on a chart, fed to a prediction, or referenced by a strategy.

An example forecast rule treats a cycle period above 20 as a trending cycle and requires the signal-to-noise reading to exceed 6, together with a positive 10-bar regression slope of close.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
17 of 26 in the Fourier analysis track
20001-6 pp.Next on Fourier analysisConstructing adaptive channel breakouts from a measured cycle periodWhen fixed lookback inputs are left at zero, entry and exit lookbacks are sized as multiples of a Hilbert-estimated period.
All readings on this track · 26 readings
  1. 1982Critiquing Fourier, Elliott, and seasonal commodity models
  2. 1982Evaluating half-hour crossovers with cycle priors and stops
  3. 1984Building moving-window spectral cycle forecasts
  4. 1988Fourier cycles versus calendar seasonal regimes
  5. 1989Constructing analog cycle signatures from price lows
  6. 1990Curve fits fail the forecast test
  7. 1991Auditing moving-average length with Fourier spectra
  8. 1991Closed-form phase for dominant-cycle spectra
  9. 1993Evaluating windowed spectral forecasts of index turning points
  10. 1994Window length for moving-window spectral forecasts
  11. 1994Constructing WAMI power and phase spectra
  12. 1994Fourier-tuned momentum filter design
  13. 1994Aliasing, leakage, and dominant-cycle reads from sampled prices
  14. 1995Constructing indicator lookbacks from Fourier spectra
  15. 1996Constructing phase from a dominant-cycle sine and cosine pair
  16. 1999Sinusoidal pseudo-securities for indicator evaluation
  17. 2000Constructing dominant cycle length from Hilbert phase
  18. 2000Constructing adaptive channel breakouts from a measured cycle period
  19. 2005Embedding forex prices into a singular-spectrum forecast basis
  20. 2005Constructing recurrent forecasts from grouped spectral components
  21. 2007Constructing a dominant cycle from transformed Fourier spectra
  22. 2010Why cycle indicators fail when parameters shift
  23. 2019Constructing futures momentum as open-interest-scaled rate of change
  24. 2019Judging a dominant cycle and a trend filter by sample, lag and the move they keep
  25. 2020Constructing futures turnover time and urgency
  26. 2020Stock power ratio as a growth trend filter
By fieldCycles and spectral analysis129 readingsBy year200085 readings
All 41 readings tagged Fourier analysis
Also on Fourier analysis5 readings
1984Building moving-window spectral cycle forecasts1984Constructing maximum-entropy spectra for dominant-cycle forecasts1986Why Fourier windows limit dominant-cycle resolution1988Fourier cycle models break in major swings1988Fourier cycles versus calendar seasonal regimes