1999issue C041-8
Fast Fourier Transform reconstruction is not a walk-forward decision tool
Fourier analysis can isolate selected frequencies and rebuild a clean waveform on a finished window. That reconstruction is not Walk-forward analysis, because later observations already shape the fitted curve at earlier dates.
- A discrete Fourier transform converts equally spaced samples into frequency-domain components so selected frequencies can be isolated or suppressed.
- A mean and a linear trend can dominate a Fast Fourier Transform magnitude spectrum and hide shorter planted cycles until the series is detrended and demeaned.
- A whole-window Fast Fourier Transform of a finished price series is not Walk-forward analysis, because later observations already influence the fitted curve at earlier dates.
- A candidate walk-forward construction keeps only each day's last sliding-window point and joins those successive endpoints into a curve that can be tested as a signal.
What the transform does
A discrete Fourier transform converts a finite series of equally spaced samples into complex frequency-domain components so that selected frequencies can be isolated or suppressed. Fast Fourier Transform computes that frequency-domain representation. Fourier analysis is the broader name for isolating or suppressing those components.
Mean, trend, and planted cycle peaks
When a constructed series still contains a mean and a linear trend, a Fast Fourier Transform magnitude spectrum can be dominated by those low-frequency terms so that known shorter cycles do not appear as peaks.
After the same constructed series is detrended and demeaned, a magnitude cutoff can retain the two planted cycle peaks, and an inverse Fast Fourier Transform can recover a close reconstruction of the original noiseless waveform.
A finished window is not Walk-forward analysis
A whole-window Fast Fourier Transform of a finished price series is not a walk-forward procedure because later observations inside that window already influence the fitted curve at earlier dates. Judging a spectral indicator on the same historical window used to choose its parameters creates an appearance of skill that a sequential, out-of-sample endpoint test is needed to challenge.
Endpoints that arrive one day at a time
A candidate walk-forward Fast Fourier Transform construction records only the last point of a sliding window that uses data up to that day, then joins those successive endpoints into a curve that can be tested as a signal.
Editorially, Walk-forward analysis is what makes that endpoint path the object of judgment. The in-window waveform is a reconstruction. Only successive endpoints are produced one day at a time.
All readings on this track · 16 readings
- 1982Building FFT spectra to size cycle filters
- 1988Fourier cycle models break in major swings
- 1988Constructing moving average filters from price Fast Fourier Transforms
- 1989Staging Fast Fourier construction under memory limits
- 1993Constructing forecast inputs with moving averages, Fourier transforms and intermarket spreads
- 1994Preprocessing prices so Fourier peaks set moving-average lengths
- 1994Constructing a spreadsheet FFT power spectrum from daily prices
- 1994Building dominant-cycle spectra with FFT preprocessing
- 1994Constructing labeled cycle lengths from FFT spectra
- 1999Fast Fourier Transform reconstruction is not a walk-forward decision tool
- 1999Walk-forward endpoint Fourier construction as a same-day mechanical procedure
- 2002From the power spectrum to indicator windows
- 2003Endpoint Fast Fourier Transform evaluation with walk-forward mechanical rules
- 2004Constructing signal and noise from market waveforms
- 2012A two-stage case study in market cycle analysis
- 2015Whitening pink noise to build a near-zero-lag cycle oscillator