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A bivariate inar(1) process with application

机译：二元inar（1）流程及其应用

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摘要

The study of time series models for count data has become a topic of special interest during the last years. However, while research on univariate time series for counts now flourishes, the literature on multivariate time series models for count data is notably more limited. In the present paper, a bivariate integer-valued autoregressive process of order 1 (BINAR(1)) is introduced. Emphasis is placed on models with bivariate Poisson and bivariate negative binomial innovations. We discuss properties of the BINAR(1) model and propose the method of conditional maximum likelihood for the estimation of its unknown parameters. Issues of diagnostics and forecasting are considered and predictions are produced by means of the conditional forecast distribution. Estimation uncertainty is accommodated by taking advantage of the asymptotic normality of maximum likelihood estimators and constructing appropriate confidence intervals for the h-step-ahead conditional probability mass function. The proposed model is applied to a bivariate data series concerning daytime and nighttime road accidents in the Netherlands.
机译：在过去的几年中，对计数数据的时间序列模型的研究已成为一个特别感兴趣的话题。然而，尽管对计数的单变量时间序列的研究现在蓬勃发展，但有关计数数据的多元时间序列模型的文献显然更为有限。在本文中，引入了阶数为1的双变量整数值自回归过程（BINAR（1））。重点放在具有二元泊松和二元负二项式创新的模型上。我们讨论了BINAR（1）模型的性质，并提出了用于估计其未知参数的条件最大似然方法。考虑诊断和预测问题，并通过条件预测分布来产生预测。通过利用最大似然估计器的渐近正态性并为h提前条件概率质量函数构造适当的置信区间，可以容纳估计不确定性。拟议的模型应用于有关荷兰白天和夜间道路交通事故的双变量数据系列。

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