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1995issue C081-5

Constructing indicator lookbacks from Fourier spectra

In this editorial reading, cycle measurement is a construction step: prepare an ordered sample, estimate spectral power with a Fourier transform, name the dominant period, and then assign indicator lengths so later rules share one horizon.

  • Preparing an ordered sample is a construction step that comes before a Fourier transform estimates cycle power and frequency.
  • Spectral analysis compares estimated power across frequencies so the dominant cycle can be named inside the sampled window.
  • That measured cycle supplies a cycle-tuned lookback, so indicator lengths and later signal spacing come from the estimate rather than from discretion.
  • Momentum spectrum equations, spreadsheet inspection of cycle, phase, and power, and Fourier review of prestored designs sit on the same construction path.
Entries in this reading3 entries
Current trackFourier analysis41 readingsSpectral analysis63 readingsDominant cycle detection180 readings

Prepare the series before the transform

Fourier analysis is the decomposition of an ordered price, volume, or breadth series into frequency components so cycle strength can be estimated over a defined lookback. Data preprocessing is the adjustment of raw observations so trend, scale, or sampling artifacts do not swamp the transform. Preparing or preprocessing the series is presented as a construction step before the transform is run. A fast Fourier transform can then be applied to the ordered market observations to estimate the power and frequency of cycles inside the series.

Compare power and name the dominant cycle

Spectral analysis is the comparison of estimated power across frequencies to see which periodicities dominate the sampled window. The dominant cycle is the period or frequency with the greatest estimated power. A measured cyclical structure is described as a basis for choosing lengths or parameters of other indicators. A cycle-tuned lookback is an indicator length taken from that measured cycle rather than chosen by discretion. The dominant cycle is then used to set indicator lengths and the spacing of later signals.

Tune a momentum design from the same estimate

Isolating the cyclical component of price data is used to tune a momentum design so its signals align with that component. Spectrum equations for a momentum design are treated as part of the same construction path as the Fourier estimate.

Inspect the transform and review stored rules

Spreadsheet worksheets are offered as a practical way to construct the transform and inspect cycle, phase, and power quantities. Fourier-based review of prestored indicator designs is framed as a method for evaluating and refining custom rules.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
14 of 26 in the Fourier analysis track
19961-2 pp.Next on Fourier analysisConstructing phase from a dominant-cycle sine and cosine pairOver one dominant cycle, a cosine-weighted sum of prices forms the real component and a sine-weighted sum over the same window forms the imaginary component.
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 year1995126 readings
All 41 readings tagged Fourier analysis
Also on Fourier analysis5 readings
1984Building moving-window spectral cycle forecasts1989Constructing analog cycle signatures from price lows1991Auditing moving-average length with Fourier spectra1991Closed-form phase for dominant-cycle spectra1993Evaluating windowed spectral forecasts of index turning points