Some notes on bootstrap method for dependent data

Abstract

Bootstrap method has emerged as a powerful tool for constructing inferential procedures for i.i.d observations. However, the assumption of having i.i.d. observations is crucial. It is easily seen that bootstrap gives incorrect answers if dependence is not taken into account. Two schemes of resampling have been developed. The first type of methods take resamples from appropriately residuals obtained by fitting a parametric or semiparametric model. These solutions have been applied with success to ARMA models. The second type of methods apply resampling to blocks of the original data to keep the dependence structure of data. The first resampling scheme is based on some model assumptions and therefore is not robust against the violation of the model. The other type of methods are less model dependent, but the applications is not still automatic. In this paper we review critically these solutions for dependent data with particularly attention to the blocking methods.