The univariate integer-valued time series has been extensively studied, but
literature on multivariate integer-valued time series models is quite limited
and the complex correlation structure among the multivariate integer-valued
time series is barely discussed. In this study, we proposed a first-order
multivariate integer-valued autoregressive model to characterize the
correlation among multivariate integer-valued time series with higher
flexibility. Under the general conditions, we established the stationarity and
ergodicity of the proposed model. With the proposed method, we discussed the
models with multivariate Poisson-lognormal distribution and multivariate
geometric-logitnormal distribution and the corresponding properties. The
estimation method based on EM algorithm was developed for the model parameters
and extensive simulation studies were performed to evaluate the effectiveness
of proposed estimation method. Finally, a real crime data was analyzed to
demonstrate the advantage of the proposed model with comparison to the other
models