EXPLORATORY MODELLING OF MULTIPLE NON-STATIONARY TIME SERIES:
LATENT PROCESS STRUCTURE AND DECOMPOSITIONS
Raquel Prado & Mike West
Final revision: December 1996
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.
Research partially supported by NSF grant
DMS-9311071. The authors are grateful to Dr Andrew Krystal, of Duke University Medical Center,
for valuable discussions and provision of data. Authors' address: Institute of Statistics and
Decision Sciences, Duke University, Durham, NC 27708--0251 U.S.A. (http://www.stat.duke.edu).
This paper appeared in Modelling Longitudinal and Spatially Correlated Data,
(ed: T. Gregoire), Springer-Verlag.
The manuscript is available in either
postscript or pdf