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2019issue C0934-37

Judging a dominant cycle and a trend filter by sample, lag and the move they keep

A short-sample cycle estimate and a long Fourier window do not run on the same clock. They can sit with a trend filter only when each tool is judged by the data it needs, the lag it adds, and whether the slower move is kept or removed.

  • A short-sample cycle estimate can be formed from about one cycle of observations, while Fourier analysis needs a much longer, more stable window and therefore answers later.
  • Because market series change, a short lookback can track the current cycle better than a long stationary transform.
  • A trend filter decides whether the slow, low-frequency part of pink-noise price is kept as a directional move or dropped so a shorter swing can be scored.
  • A predictive filter fades quickly more than two or three bars ahead, so the cycle-plus-filter pairing is a statistical setup rather than a long forecast.
Entries in this reading3 entries
Current trackFourier analysis41 readingsDominant cycle detection180 readingsTrend filter184 readings

Three tools that do not share a clock

A dominant cycle is a short-sample estimate of the strongest repeating component in recent price data. It is used as a local timing baseline rather than a long-history spectrum. A trend filter is a rule that keeps or removes the slower component of price so a strategy can stay with a directional move or isolate a shorter swing. Fourier analysis is a transform that estimates frequency content from a long, relatively stable sample and therefore adds delay when the series is still changing.

A short-sample spectrum method can estimate a local cycle from about one cycle of observations, whereas a Fourier transform needs a much longer window. Because market series change over time, a short lookback can track the current cycle better than a long stationary transform.

Pink noise and the move the filter may keep

Price series can be treated as pink noise: not fully random, with more energy at lower frequencies, so trends can be read as long-cycle segments rather than a separate process. Sine-wave primitives are used to isolate tradable cycles inside that noise and to give a probabilistic location on the wave. Other shapes can be built from the same primitives.

A market model can drop high-frequency chatter and, when swing trading, can also drop trend information so the remaining cycle component is easier to score. Editorial reading: the trend filter is the switch for that choice, keeping the slower component when the aim is a directional move and removing it when the aim is a shorter swing.

A statistical setup, not a long forecast

A predictive filter applied more than two or three bars ahead degrades quickly, so a cycle-plus-filter model is better framed as a statistical setup than as a long forecast.

Percent wins and profit factor are treated as the two primitive performance measures. Several other ratios can be derived from that pair, while an equity curve is a poor first check. Mean-reversion or short-hold swing rules tend to post a higher win rate but a lower profit factor because trades are not left open long enough to capture a full trend move.

When a simpler filter is the better clock

A more complex black-box filter, including a Fourier-style estimator, needs more data and therefore answers later. A simpler filter is preferred when a usable, low-delay output matters more than extra refinement.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
24 of 26 in the Fourier analysis track
20208-13 pp.Next on Fourier analysisConstructing futures turnover time and urgencyInertia is total reported open interest across all contract months, equal to the number of longs and to the number of shorts, and is treated as resistance to starting or stopping a move.
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 fieldIndicators and filters874 readingsBy year2019140 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