Statistics and Its Interface

Volume 16 (2023)

Number 1

Special issue on recent developments in complex time series analysis – Part I

Guest editors: Robert T. Krafty (Emory Univ.), Guodong Li (Univ. of Hong Kong), Anatoly Zhigljavsky (Cardiff Univ.)

Hierarchical dynamic PARCOR models for analysis of multiple brain signals

Pages: 69 – 79

DOI: https://dx.doi.org/10.4310/21-SII699

Authors

Wenjie Zhao (PhD Candidate, Department of Statistics, University of California, Santa Cruz, Cal., U.S.A.)

Raquel Prado (Professor, Department of Statistics, University of California, Santa Cruz, Cal., U.S.A.)

Abstract

We present an efficient hierarchical model for inferring latent structure underlying multiple non-stationary time series. The proposed model describes the time-varying behavior of multiple time series in the partial autocorrelation domain, which results in a lower dimensional representation, and consequently computationally faster inference, than those required by models in the time and/or frequency domains, such as time-varying autoregressive models, which are commonly used in practice. We illustrate the performance of the proposed hierarchical dynamic PARCOR models and corresponding Bayesian inferential procedures in the context of analyzing multiple brain signals recorded simultaneously during specific experimental settings or clinical studies. The proposed approach allows us to efficiently obtain posterior summaries of the time-frequency characteristics of the multiple time series, as well as those summarizing their common underlying structure.

Keywords

multiple non-stationary time series, partial autocorrelation, hierarchical Bayesian models, dynamic linear models

Received 1 April 2021

Accepted 16 August 2022

Published 28 December 2022