A bivariate first-order signed integer-valued autoregressive process

Bivariate integer-valued time series occur in many areas, such as finance, epidemiology, business etc. In this paper, we present bivariate autoregressive integer-valued time series models, based on the signed thinning operator. Compared to classical bivariate INAR models, the new processes have the advantage to allow for negative values for the time series and the autocorrelation functions. Strict stationarity and ergodicity of the processes are established. The moments and the autocovariance functions are determined. Some methods for estimating the model parameters are considered and the asymptotic properties of the obtained estimators are derived. Simulation experiments as well as analysis of real data sets are carried out to assess the models' performance