Zero-inflated, hurdle and bivariate parameter-driven count models

A time series is a collection of observations made sequentially through time. Examples occur in a variety of fields, ranging from medicine to engineering. The analysis of time series of counts is one of the rapidly developing areas in time series modeling. In time series, it is unlikely that neighbouring observations are independent. To accommodate potential correlation for count data, two main classes of models are frequent in the literature: parameter-driven and observation-driven models. Central to both classes are the generalized linear models (GLMs). Parameter-driven models result when temporal random effects are used in the GLM to accommodate the autocorrelations. In this dissertation we propose zero-inflated and hurdle specifications for both Poisson and negative binomial parameter-driven models. We employ the data cloning approach as the numerical tool for performing inferences about the models. We carry out intensive simulations to examine the performance of the proposed methodologies. An application of the methods to a data set on the daily counts of emergency department visits for asthma cases in Ontario, Canada, is also provided. The second focus of this dissertation is to model dependence in bivariate time series of counts. In this direction, we propose two parameter-driven models based on a commonly used bivariate Poisson specification. The first model employs one latent process through the cross-correlation parameter of the bivariate Poisson distribution, thus leading to common temporal autocorrelations between the components of the bivariate Poisson, while the second model uses two latent processes to introduce separate autocorrelations in the two marginal processes. An intensive simulation study and real data applications are also provided in these scenarios