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A new multivariate integer-valued Generalized AutoRegressive ConditionalHeteroscedastic process based on a multivariate Poisson generalized inverseGaussian distribution is proposed. The estimation of parameters of the proposedmultivariate heavy-tailed count time series model via maximum likelihood methodis challenging since the likelihood function involves a Bessel function thatdepends on the multivariate counts and its dimension. As a consequence,numerical instability is often experienced in optimization procedures. Toovercome this computational problem, two feasible variants of theExpectation-Maximization (EM) algorithm are proposed for estimating parametersof our model under low and high-dimensional settings. These EM algorithmvariants provide computational benefits and help avoid the difficult directoptimization of the likelihood function from the proposed model. Our model andproposed estimation procedures can handle multiple features such as modeling ofmultivariate counts, heavy-taildness, overdispersion, accommodation ofoutliers, allowances for both positive and negative autocorrelations,estimation of cross/contemporaneous-correlation, and the efficient estimationof parameters from both statistical and computational points of view. ExtensiveMonte Carlo simulation studies are presented to assess the performance of theproposed EM algorithms. An application to modeling bivariate count time seriesdata on cannabis possession-related offenses in Australia is discussed.

A multivariate heavy-tailed integer-valued GARCH process with EM algorithm-based inference