Bayesian Model Search for Nonstationary Periodic Time Series

TL;DR

This paper introduces a Bayesian approach using trans-dimensional MCMC to detect change-points and changing periodicities in nonstationary oscillatory time series, demonstrated on sleep and health data.

Contribution

It develops a novel Bayesian piecewise oscillatory model with an MCMC algorithm for joint change-point and periodicity estimation in nonstationary time series.

Findings

Successfully identified ultradian oscillations in skin temperature during sleep.

Detected sleep apnea episodes in respiratory traces.

Validated methodology on health-related time series data.

Abstract

We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behaviour. We approximate the time series using a piecewise oscillatory model with unknown periodicities, where our goal is to estimate the change-points while simultaneously identifying the potentially changing periodicities in the data. Our proposed methodology is based on a trans-dimensional Markov chain Monte Carlo (MCMC) algorithm that simultaneously updates the change-points and the periodicities relevant to any segment between them. We show that the proposed methodology successfully identifies time changing oscillatory behaviour in two applications which are relevant to e-Health and sleep research, namely the occurrence of ultradian oscillations in human skin temperature during the time of night rest, and the detection of instances of sleep apnea in plethysmographic respiratory traces.