ABSTRACT
We have seen a tremendous increase in models for discrete-valued time series over the past few decades. Although there is a flourishing literature on models and methods for univariate integer-valued time series, the literature is rather sparse for the multivariate case, especially for multivariate count time series. Multivariate count data occur in several different disciplines like epidemiology, marketing, criminology, and engineering, just to name a few. For example, in syndromic surveillance systems, we record the number of patients with a given symptom. An abrupt change in this number could indicate a threat to public health, and our goal would be to discover such a change as early as possible. In practice, a large number of symptoms are counted creating possibly associated multiple time series of counts. An adequate analysis of such multiple time series requires models that can take into account the correlation across time as well as the correlations between the different symptoms.
