Computationally efficient segmentation for non-stationary time series with oscillatory patterns

TL;DR

This paper introduces a fast, Fourier-based segmentation method for non-stationary oscillatory time series, improving efficiency over existing techniques while maintaining accuracy, with applications in climate and EEG data analysis.

Contribution

It presents a novel discretization approach that simplifies change-point detection in oscillatory time series, avoiding complex MCMC algorithms used previously.

Findings

Significantly faster than existing methods

Maintains comparable accuracy in change-point detection

Provides theoretical bounds on localization error

Abstract

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of sinusoidal functions with unknown frequencies and amplitudes plus noise. The inference for this model is non-trivial. However, discretising the parameter space allows us to recast this complex estimation problem into a more tractable linear model, where the covariates are Fourier basis functions. Then, any change-point detection algorithms for segmentation can be used. The advantage of our proposal is that it bypasses the need for trans-dimensional Markov chain Monte Carlo algorithms used by state-of-the-art methods. Through simulations, we demonstrate that our method is significantly faster than existing approaches while maintaining comparable numerical accuracy. We also provide high probability bounds on the change-point localization error. We apply our methodology to climate and EEG sleep data.