Bayesian Model Search for Nonstationary Periodic Time Series

Beniamino Hadj-Amar, Bärbel Finkenstädt Rand, Mark Fiecas, Francis Lévi, Robert Huckstepp

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We propose a novel Bayesian methodology for analyzing nonstationary time series that exhibit oscillatory behavior. 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 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 behavior 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. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1320-1335
Number of pages16
JournalJournal of the American Statistical Association
Issue number531
StatePublished - Jul 2 2020

Bibliographical note

Funding Information:
B. Hadj-Amar was supported by the Oxford-Warwick Statistics Programme (OxWaSP) and the Engineering and Physical Sciences Research Council (EPSRC) under grant number EP/L016710/1. B. Finkenstädt and F. Lévi were supported by the Medical Research Council (MRC), grant reference: MR/M013170/1. F. Lévi was partly supported by the Conseil Régional d’Île de France, the Conseil Régional de Champagne-Ardenne, Mairie de Paris and the Banque Publique d’Investissement (BPI France) through the Fonds Unique Interministériel 12 (PiCADo, contract 11017951), and the Institut de Recherches en Santé Publique from France (CLOCK-DOM1, grant 2014-BDCR-EC). R. Huckstepp was supported by the MRC, grant reference: MC/PC/15070. We wish to thank the referees, the associate editor, Dr. Paul Jenkins, Zeda Li, and Jack Jewson for their insightful and valuable comments. The work presented in this article was developed as part of the first author’s PhD thesis at the University of Warwick.

Publisher Copyright:
© 2019 The Author(s). Published with license by Taylor & Francis Group, LLC.


  • Bayesian spectral analysis
  • Change-points
  • Reversible-jump MCMC
  • Sleep apnea
  • Ultradian sleep cycles


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