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1990issue C011-2

Curve fits fail the forecast test

A nonlinear description can specify a historical path with concise equations and still leave later position and trajectory unpredicted. For forecasting, that style is treated as a curve fit, and a chaos-style search is classed with any other system optimization.

  • A nonlinear description can specify a historical path with concise equations and still leave later position and trajectory unpredicted.
  • For forecasting, that descriptive style is treated as functionally equivalent to a polynomial curve fit, and a chaos-style search is classed with any other system optimization.
  • The butterfly effect is offered as the reason a tiny early difference can produce a large later divergence, so coefficients look more meaningful when favorable results cluster across a range.
  • If noise were truly removed, moving averages and Fast Fourier tools would no longer be needed, and whether the equations match the forces that move markets is left unresolved.
Entries in this reading3 entries
Current trackFourier analysis41 readingsSystem optimization131 readingsMoving average597 readings

Description is not a forecast

A nonlinear description can specify a historical path with concise equations and still leave later position and trajectory unpredicted. For forecasting, that descriptive style is treated as functionally equivalent to a polynomial curve fit.

Fitting a curve to already-known data does not guarantee predictive value. A curve fit can be an elegant description of already-seen data, written in short equations, without implying a usable forecast.

Sensitivity to starting values

Extreme sensitivity to initial conditions is offered as the reason a tiny early difference can produce a large later divergence, breaking scaled linear cause and effect. The butterfly effect is that claim: a tiny change in starting conditions can produce a large later divergence in a nonlinear path.

Baselines stay until noise is gone

If noise were truly removed from a time series, conventional moving averages and Fast Fourier tools would no longer be needed. Fourier analysis is a spectral decomposition of ordered prices or related series, treated here as a conventional baseline that becomes redundant if noise is truly gone. A moving average is a conventional smoother of ordered observations, treated here as disposable once a series is assumed to be cleaned of noise.

Optimization is still optimization

A chaos-style optimization is classed with any other system optimization. System optimization is the joint testing of entry, exit and abstention rules against known outcomes. A strong in-sample score is not evidence of later usefulness.

Clustered results, unresolved forces

Coefficient values are judged more likely to be meaningful when favorable results cluster across a range, especially in a bell-shaped pattern. Result clustering is that heuristic: coefficient choices look more credible when favorable outcomes concentrate across a range.

Whether a nonlinear equation system corresponds to the forces that actually move markets is left unresolved, so understanding the mathematics and its concepts is treated as a prerequisite.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
6 of 26 in the Fourier analysis track
19911-5 pp.Next on Fourier analysisAuditing moving-average length with Fourier spectraFourier analysis is presented as a way to inspect cyclical content and to choose trend-following indicator lengths. Its forecasting use is described as limited.
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 fieldTime series and forecasting58 readingsBy year1990142 readings
All 41 readings tagged Fourier analysis
Also on Fourier analysis5 readings
1994Fourier-tuned momentum filter design1988Constructing moving average filters from price Fast Fourier Transforms1999Sinusoidal pseudo-securities for indicator evaluation1982Building FFT spectra to size cycle filters1982Critiquing Fourier, Elliott, and seasonal commodity models