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.

翻译：单变量整数值时间序列已被广泛研究，但关于多元整数值时间序列模型的文献相当有限，且多元整数值时间序列之间复杂的相关结构鲜有讨论。本研究提出了一阶多元整数值自回归模型，以更灵活地刻画多元整数值时间序列之间的相关性。在一般条件下，我们建立了所提模型的平稳性和遍历性。基于所提方法，我们讨论了具有多元泊松-对数正态分布和多元几何-逻辑正态分布的模型及其相应性质。开发了基于EM算法的参数估计方法，并通过大量模拟研究评估了所提估计方法的有效性。最后，通过真实犯罪数据分析，并与其它模型比较，证明了所提模型的优势。