Statistical inference of pth-order generalized binomial autoregressive model

To capture the higher-order autocorrelation structure for finite-range integer-valued time series of counts, and to consider the interdependence between individuals, a pth-order generalized binomial autoregressive (GBAR(p)) process is proposed in this paper. The stationarity and ergodicity of the GBAR(p) model are proved, and the basic probabilistic and statistical properties of the model are discussed. The unknown parameters are estimated by the conditional least squares and conditional maximum likelihood methods. The performances of two kinds of estimators are studied via simulations, and the forecasting problem of this model is also considered in this paper. Finally, the model is applied to a real data set and compared with some existing models to investigate the rationality of the GBAR(p) model.