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1989issue C041-5

Constructing analog cycle signatures from price lows

A paper overlay stacks selected cyclical lows into a cycle-signature. Tick height, scatter, and one-sided smear show regularity and timing, while a power-spectrum peak still records amplitude.

  • A cycle-signature can be assembled by hand from turning-point marks, while Fourier-style and maximum-entropy work produce an amplitude spectrum that ordinarily requires a computer.
  • Signature-height records how regularly a cycle repeats. It is not the same as a power-spectrum peak and does not by itself mean a large price change.
  • Scattered ticks, even stacks, loose clusters, out-of-phase components, and period-smear each change the width of the next-low timing-window.
  • A next-low timing-window is projected by pairing the first two overlay cycles with the last two chart lows. Reverse-modeling draws known mixtures first so a live signature has a template.
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Current trackFourier analysis41 readingsSpectral analysis63 readingsDominant cycle detection180 readings

A hand-built cycle-signature

Fourier-style and maximum-entropy cycle work produce an amplitude spectrum that ordinarily requires a computer. A cycle-signature can be assembled by hand from turning-point marks.

The overlay is built from a price history that already shows several selected cyclical lows. A start mark is seated on one low, later lows are transferred as ticks, and the start mark is walked forward so a stable cycle reprints ticks in nearly the same places. The dominant-cycle is the interval that stays most consistent after those successive lows are aligned on the overlay.

Signature-height and tick scatter

Overlay-mark height records how regularly a cycle repeats, whereas a power-spectrum peak records amplitude. A tall signature does not by itself mean a large price change. Signature-height is a regularity cue rather than a measure of spectral amplitude.

Scattered ticks correspond to no coherent cycle, comparable to white noise that would lie flat across frequencies on a spectrum. Evenly stacked tall ticks correspond to a regular sine-like period. A looser cluster widens the zone of the next possible low, and that band of dates is the timing-window.

Phase conflict, composites, and period-smear

A regular cycle that is out of phase with other components still produces a wide timing-window. Combined sine-like waves of different frequencies leave one composite signature, whereas a power spectrum of the same mixture would show separate spikes. Each family's length is read from its own first spike to the next, and long cycles appear only if marks extend far enough.

The overlay is most usable when target cycle lengths are chosen in advance. Lengthening or shortening periods appear as ticks that smear to one side. That one-sided drift is period-smear.

Projecting the next-low timing-window

A next-low timing-window is read by aligning the first two overlay cycles with the last two chart lows so the third overlay cycle projects ahead. Pairing those two cycles and matching their width is the alignment rule, and that pairing is checked against earlier turning points.

Reverse-modeling as a comparison template

Hypothetical cycle mixtures can be drawn first so their signatures, including phase shifts, period changes, and amplitude variation, become templates for comparison. Reverse-modeling means drawing the overlay a chosen mix of sine-like cycles would leave, including phase and period changes, so a live signature can be compared with a known template.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
5 of 26 in the Fourier analysis track
19901-2 pp.Next on Fourier analysisCurve fits fail the forecast testA nonlinear description can specify a historical path with concise equations and still leave later position and trajectory unpredicted.
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 year1989126 readings
All 41 readings tagged Fourier analysis
Also on Fourier analysis5 readings
1984Building moving-window spectral cycle forecasts1991Auditing moving-average length with Fourier spectra1991Closed-form phase for dominant-cycle spectra1993Evaluating windowed spectral forecasts of index turning points1994Aliasing, leakage, and dominant-cycle reads from sampled prices