Time series of (small) counts are common in practice and appear in a wide variety of fields. In the last three decades, several models that explicitly account for the discreteness of the data have been proposed in the literature. However, for multivariate time series of counts several difficulties arise and the literature is not so detailed. This work considers Bivariate INteger-valued Moving Average, BINMA, models based on the binomial thinning operation. The main probabilistic and statistical properties of BINMA models are studied. Two parametric cases are analysed, one with the cross-correlation generated through a Bivariate Poisson innovation process and another with a Bivariate Negative Binomial innovation process. Moreover, parameter estimation is carried out by the Generalized Method of Moments. The performance of the model is illustrated with synthetic data as well as with real datasets.

中文翻译：

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基于二项式细化操作的二元整数值移动平均模型推断

（小）计数的时间序列在实践中很常见，并且出现在各种领域。在过去的三年中，文献中提出了几种明确解释数据离散性的模型。然而，对于多变量时间序列的计数，会出现一些困难，并且文献不是那么详细。这项工作考虑了基于二项式细化操作的双变量整数值移动平均线 (BINMA) 模型。研究了 BINMA 模型的主要概率和统计特性。分析了两个参数案例，一个是通过二元泊松创新过程产生的互相关，另一个是二元负二项式创新过程。此外，参数估计是通过广义矩法进行的。