Exploratory Modelling of Multiple Non-Stationary Time Series: Latent Process Structure and Decompositions

Abstract

We describe and illustrate Bayesian approaches to modelling and analysis of multiple non-stationary time series. This begins with univariate models for collections of related time series assumedly driven by underlying but unobservable processes, referred to as dynamic latent factor processes. We focus on models in which the factor processes, and hence the observed time series, are modelled by time-varying autoregressions capable of flexibly representing ranges of observed non-stationary characteristics. We highlight concepts and new methods of time series decomposition to infer characteristics of latent components in time series, and relate univariate decomposition analyses to underlying multivariate dynamic factor structure. Our motivating application is in analysis of multiple EEG traces from an ongoing EEG study at Duke. In this study, individuals undergoing ECT therapy generate multiple EEG traces at various scalp locations, and physiological interest lies in identifying dependencies and dissimilarities across series. In addition to the multivariate and non-stationary aspects of the series, this area provides illustration of the new results about decomposition of time series into latent, physically interpretable components; this is illustrated in data analysis of one EEG data set. The paper also discusses current and future research directions.