Residual Analysis with Bivariate INAR(1) Models

Abstract

In this paper we analyze forecasting errors made by random coefficients bivariate integer-valued autoregressive models of order one. These models are based on the thinning operator to support discreteness of data. In order to achieve a comprehensive analysis, we introduce a model that implements a binomial as well as a negative binomial thinning operator. There are two components of the model: survival and innovation. Forecasting errors made by each of these two sources of uncertainty are unobservable in the classic way. Thus, we derive predictive distributions from which we obtain the expected value of each component of the model. We provide an example of residual analysis on real data.