1988issue C091-3
Constructing moving average filters from price Fast Fourier Transforms
A historical reply treated Fourier analysis of stock and commodity series as a construction sequence. Daily closes are pre-processed, a Fast Fourier Transform recovers amplitude and phase, and that result specifies a moving average chosen to suppress noise in the past series.
- Fourier analysis decomposes an ordered price series into constituent frequencies together with their amplitudes and phases.
- The construction pre-processes historical daily closing prices, applies a Fast Fourier Transform, and uses the result to specify a moving average that suppresses noise in the past series.
- After that historical filter is specified, a similar future noise level is assumed and the moving average is then used as a trading tool.
- Amplitude and phase recovered from the historical series cannot be unwrapped sequentially into the future with statistical accuracy.
This archive note restates a historical reply on Fourier analysis of stock and commodity series. The reply described a sequence that starts with daily closes and ends with a moving average specified from a Fast Fourier Transform.
What the reader asked
A reader asked whether analytic work used Fourier transforms or Fourier analysis of frequencies, phases, and amplitudes, and whether a simple Fourier analysis program could be obtained.
The reply stated that Fourier analysis had been applied to historical stock and commodity series. In this setting, Fourier analysis is the decomposition of an ordered price series into constituent frequencies together with their amplitudes and phases.
From pre-processing to a moving average
The described construction begins with pre-processing, the preparation of historical daily closing prices before the transform is run. A Fast Fourier Transform is then applied to those prepared closes. The Fast Fourier Transform is a computational transform used to recover the spectral breakdown of the series.
The transform result is used to design a filter, including a moving average, chosen to suppress noise in the past series. The moving average is a smoother specified from that spectral result. After the historical filter is specified, a similar future noise level is assumed and the moving average is then used as a trading tool.
Amplitude, phase, and serial unwrapping
A Fast Fourier Transform decomposes historical data into amplitude and phase. Amplitude is the strength of a frequency component recovered from the historical series. Phase is the timing alignment of a frequency component recovered from the historical series.
The same reply stated that those amplitude and phase components cannot be unwrapped sequentially into the future with statistical accuracy. Serial unwrapping is an attempt to extend recovered amplitude and phase components forward as a continuing series.
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