Frequency-Domain Filters for Financial Time-Series Features
Summary
This article explains how to filter financial time series in the frequency domain: preprocess a finite series, apply a fast Fourier transform, modify frequency components with a filter response, then invert the transform and undo preprocessing. It describes Gaussian-shaped filters and bandpass, lowpass, and highpass forms, along with in-phase filters that preserve timing and in-quadrature filters that shift phase by 90 degrees. Paired quadrature-mirror outputs can be combined to estimate a localized periodic component’s amplitude and phase.
The examples illustrate how quadrature output can highlight rapid changes that are less apparent in the in-phase result. The discussion also covers padding and detrending: the DFT treats input as periodic, so finite or slowly varying data can cause wraparound effects and spectral leakage. Padding can improve frequency resolution and FFT efficiency, but unsuitable padding values can introduce artifacts. The material is primarily a signal-processing explanation with implementation examples; it provides no systematic trading performance test, and filter choice depends on the application and careful handling of preprocessing distortions.
Key ideas
- Frequency-domain filtering transforms a series with an FFT, applies frequency-dependent coefficients, and transforms the result back.
- In-phase filters preserve the input’s phase relationship, while in-quadrature filters shift phase and can emphasize rapid changes.
- Combining in-phase and in-quadrature outputs allows amplitude and phase analysis of localized periodic components.
- Padding and detrending help manage finite-series effects, though poor preprocessing can contaminate the spectrum.
- Gaussian response shapes offer smoother transitions, but filter parameters and shape should reflect the analysis need.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.