Silva Isabel, Eduarda Silva Maria, Torres Cristina
Faculdade de Engenharia da Universidade do Porto and CIDMA, Porto, Portugal.
Faculdade de Economia da Universidade do Porto and CIDMA, Porto, Portugal.
J Appl Stat. 2020 Apr 1;47(13-15):2546-2564. doi: 10.1080/02664763.2020.1747411. eCollection 2020.
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.
（小）计数的时间序列在实际中很常见，并且出现在各种各样的领域。在过去三十年中，文献中提出了几种明确考虑数据离散性的模型。然而，对于多变量计数时间序列会出现几个困难，并且文献对此阐述得并不详细。这项工作考虑基于二项式稀疏运算的二元整数值移动平均（BINMA）模型。研究了BINMA模型的主要概率和统计性质。分析了两种参数情况，一种是通过二元泊松创新过程产生互相关，另一种是通过二元负二项式创新过程产生互相关。此外，通过广义矩方法进行参数估计。用合成数据以及真实数据集说明了该模型的性能。
