Multivariate Time Series Modeling and Classi cation via Hierarchical VAR Mixtures

A novel class of models for multivariate time series is presented. We consider hier-archical mixture-of-expert (HME) models in which the experts, or building blocks of the model, are vector autoregressions (VAR). It is assumed that the VAR-HME model partitions the covariate space, specically including time as a covariate, into overlapping regions called overlays. In each overlay a given number of VARs com-pete with each other so that the most suitable model for the overlay is favored by a large weight. The weights have a particular parametric form that allows the modeler to include relevant covariates. Maximum likelihood estimation of the parameters is achieved via the EM (expectation-maximization) algorithm. The number of over-lays, the number of models and the model orders of the VARs that dene a particular VAR-HME model conguration are chosen by means of an algorithm based on the Bayesian information criterion (BIC). Issues of model checking and inference of latent structure in multiple time series are investigated. The new methodology is illustrated by analyzing a synthetic data set and a 7-channel electroencephalogram data set