A copula based BINAR(1) process with applications

The application of the simple first order integer-valued autoregressive model to multidimensional space allows the simultaneous modelling of multiple series. Despite this, existing models do not provide a great deal of flexibility for modelling dependence, allowing only positive correlations to be modelled. A copula is one of the most widely used tools in statistics to describe, analyze and model the relationship between random variables. As part of this study, we investigate a bivariate first order integer-valued autoregressive process in which cross-correlations are introduced through the use of copulas for the specification of the joint distribution of innovations. Throughout the paper, we emphasize the parametric case arising from the Poisson extended exponential marginals. An empirical illustration is provided using a bivariate financial time series and a bivariate criminal dataset.