Flexible Bivariate INAR(1) Processes Using Copulas

Multivariate count time series data occur in many different disciplines. The class of INteger-valued AutoRegressive (INAR) processes has the great advantage to consider explicitly both the discreteness and autocorrelation characterizing this type of data. Moreover, extensions of the simple INAR(1) model to the multi-dimensional space make it possible to model more than one series simultaneously. However, existing models do not offer great flexibility for dependence modelling, allowing only for positive correlation. In this work, we consider a bivariate INAR(1) (BINAR(1)) process where cross-correlation is introduced through the use of copulas for the specification of the joint distribution of the innovations. We mainly emphasize on the parametric case that arises under the assumption of Poisson marginals. Other marginal distributions are also considered. A short application on a bivariate financial count series illustrates the model.     

On Estimation of the Bivariate Poisson INAR Process

In a recent article, Pedeli and Karlis (2010 Pedeli, X. and Karlis, D. 2010. A Bivariate INAR(1) Process with Application. Statistical Modelling: An international Journal, 11: 325–349. [Crossref], [Web of Science ®] , [Google Scholar]) examined the extension of the classical Integer–valued Autoregressive (INAR) model to the bivariate case. In the present article, we examine estimation methods for the case of bivariate Poisson innovations. This is a simple extension of the classical INAR model allowing for two discrete valued time series to be correlated. Properties of different estimators are given. We also compare their properties via a small simulation experiment. Extensions to incorporate covariate information is discussed. A real data application is also provided.