2015issue C0122
Whitening pink noise to build a near-zero-lag cycle oscillator
A step-like price change has a Fourier-domain response that falls as the reciprocal of frequency, matching pink noise. Whitening that spectrum and then applying a low-lag smoother yields a universal oscillator described as muting gap openings while turning points remain visible.
- A step-like price change has a Fourier-domain response that falls as the reciprocal of frequency, matching the spectrum of pink noise.
- Whitening an oscillator spectrum tends to suppress gap-opening artifacts in the indicator output.
- A construction path starts from a uniform-amplitude white spectrum and then applies a low-lag smoother to obtain a universal oscillator.
- The constructed oscillator is described as having essentially zero lag, as usable for identifying trends, and as tracking turning points without harsh gap reactions.
Start from the spectrum of a price step
A step-like price change has a Fourier-domain response that falls as the reciprocal of frequency. That shape matches the spectrum of pink noise, a noise process whose spectral amplitude falls as frequency rises.
Market series can be modeled as pink noise whose degree of coloring can change over time. Frequency here means the number of complete cycles observed in a chosen time unit.
Editorial note: TradersWeek treats ordinary price steps as a colored spectrum first, not as clean sinusoids that are already ready for turning-point rules.
Flatten the spectrum before reading turns
Spectral analysis is the study of how amplitude is distributed across frequency, including the reciprocal-of-frequency shape associated with pink noise and the whitening step that flattens that spectrum.
Whitening an oscillator spectrum tends to suppress gap-opening artifacts in the indicator output.
Decompose the series and name the dominant cycle
A Fast Fourier Transform is a decomposition of an ordered series into sinusoids of different cycle lengths, each a fraction of a shared fundamental period.
The dominant cycle is the cycle length that accounts for the strongest periodic component once a series has been viewed in the frequency domain.
Synthesize a universal oscillator
A construction path starts from a uniform-amplitude white spectrum and then applies a low-lag smoother to obtain a universal oscillator. That indicator is obtained by synthesizing a white spectrum and then applying a low-lag smoother so gap openings are muted while turning points remain visible.
Lag is how many observations a filter trails its input. The construction aims for essentially zero lag at the oscillator output. The constructed oscillator is described as having essentially zero lag and as usable for identifying trends.
On 15-minute regular-session index-futures bars, the constructed oscillator is described as avoiding harsh gap reactions while still tracking intraday turning points.
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