Some models for multivariate time series for counts

Abstract

In many fields data are presented that evolve together over time. Such datacan be the prices of some shares on the stock exchange, the murders in different regions for a certain period of time or the arrivals at the differentairports of a specific country. In the literature there are categories of modelscapable of describing such data as parameter driven models and observationdriven models. Observation driven models are very popular for describingsuch data due to their ease in estimating parameters which is not true forparameter driven models. In this thesis, to emphasizing the advantages of parameter driven models, we present some of them that are flexible to describedata that evolve over time and describe cross-correlation, autocorrelationand overdispersion. Specifically, we will describe five parameter driven models, the State Space Multivariate Poisson model (SSMP), a doubly stochasticmodel with latent factors, multivariate Poisson scaled beta (MPSB) models, a dynamic factor model and the hierarchical Markov switching model(HMSM). All models to be presented are models that use modern numericalmethods for parameter estimation and the suitability of these methods hasbeen documented with examples.