Estimation and Forecasting in INAR(P) Models Using Sieve Bootstrap

Abstract

In this paper we analyse some bootstrap techniques to make inference in INAR(p) models. First of all, via Monte Carlo experiments we compare the performances of these methods when estimating the thinning parameters in INAR(p) models. We state the superiority of sieve bootstrap approaches on block bootstrap in terms of low bias and Mean Square Error (MSE). Then we apply the sieve bootstrap methods to obtain coherent predictions and confidence intervals in order to avoid difficulty in deriving the distributional properties. Keywords INAR(p) models, estimation, forecast, bootstrap JEL Codes C22, C53 AbstractIn this paper we analyse some bootstrap techniques to make inference in INAR(p) models. First of all, via Monte Carlo experiments we compare the performances of these methods when estimating the thinning parameters in INAR(p) models. We state the superiority of sieve bootstrap approaches on block bootstrap in terms of low bias and Mean Square Error (MSE). Then we apply the sieve bootstrap methods to obtain coherent predictions and confidence intervals in order to avoid difficulty in deriving the distributional properties.

Bootstrapping INAR models

“…where " • " denotes mutually independent binomial thinning operations executed independently of everything else; see Bisaglia and Gerolimetto (2016) for such an approach. But again, this approach is not applicable, because, among others, the residuals 1+p , .…”