Bootstrapping Bivariate INAR Models with Applications

Bivariate Integer Autoregressive Models (B-INAR), formally introduced in Pedeli and Karlis, can be a flexible tool to deal with integer-valued time series exhibiting correlation in time. In this context, different parametric assumptions for the innovations can be carried out basing on the features of the series. For instance, Poisson distributions (BP-INAR) can be used in the case of equidispersed processes, while Negative Binomial (BNB-INAR) and Binomial (BB-INAR) innovations help to consider the presence of overdispersion and underdispersion, respectively. The aim of this work is to explore the potential of bootstrap methods to improve inference in B-INAR models considering (bias-corrected) parameter estimation, variance estimation, hypothesis testing, and forecasting. Either parametric or semi-parametric methods can be employed in the bootstrap algorithms, also considering different distributions for the innovation processes. Performance of bootstrap methods are investigated through Monte Carlo simulations and compared (where available) with asymptotic methods. Usefulness of proposed methods is shown through empirical applications.