Integer valued autoregressive (INAR) models have important part in time series of counts analysis. These models are composed of two components: survival process and innovation process. Survival component is based on thinning operator where the most used ones are binomial thinning and negative binomial thinning operators. In a situation where two time series are cross-correlated bivariate INAR models should be introduced. We present bivariate models based on binomial as well as negative binomial thinning operators.
Innovation processes of these models are introduce in a manner to satisfy stationarity condition. Statistical properties of the models are discussed. Tests on a real data are conducted to demonstrate practical aspect of the models. Forecasting error is analyzed where special attention is payed on error made by survival component and error made by innovation component. Based on this residual analysis some aspects of future research are discussed.