Modelling multivariate time series for count data
Abstract
The study of time series models for count data has become a topic of special interest during the last years. However, while research on univariate time series for counts now flourishes, the literature on multivariate time series models for count data is notably more limited. The main reason for this is that the analysis of multivariate counting processes presents many more difficulties. Specifically, the need to account for both serial and cross-correlation complicates model specification, estimation and inference. This thesis deals with the class of INteger-valued AutoRegressive (INAR) processes, a recently popular class of models for time series of counts. The simple, univariate INAR(1) process is initially extended to the 2-dimensional space. In this way, a bivariate (BINAR(1)) process is introduced. Subsequently, the time invariant BINAR(1) model is generalized to a BINAR(1) regression model. Emphasis is given on models with bivariate Poisson and bivariate negative binomial innovat ...
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