Bootstrap Confidence Intervals for the INAR(p) Process

Abstract

The distributional properties of forecasts in an integer-valued time series model have not been discovered yet mainly because of the complexity arising from the binomial thinning operator. We propose two bootstrap methods to obtain nonparametric prediction intervals for an integer-valued autoregressive model : one accomodates the variation of estimating parameters and the other does not. Contrary to the results of the continuous ARMA model, we show that the latter is beter than the former in forecasting the future values of the integer-valued autoregressive model.