Modeling of multivariate time series using hidden Markov models.

摘要

Vector-valued (or multivariate) time series data commonly occur in various sciences. While modeling univariate time series is well-studied, modeling of multivariate time series, especially finite-valued or categorical, has been relatively unexplored. In this dissertation, we employ hidden Markov models (HMMs) to capture temporal and multivariate dependencies in the multivariate time series data. We modularize the process of building such models by separating the modeling of temporal dependence, multivariate dependence, and non-stationary behavior. We also propose new methods of modeling multivariate dependence for categorical and real-valued data while drawing parallels between these two seemingly different types of data. Since this work is in part motivated by the problem of prediction precipitation over geographic regions from the multiple weather stations, we present in detail models pertinent to this hydrological application and perform a thorough analysis of the models on data collected from a number of different geographic regions.