Introducing model uncertainty in time series bootstrap

Abstract

It is common in parametric bootstrap to select the model from the data, and then treat it as it were the true model. Kilian (1998) have shown that ignoring the model uncertainty may seriously undermine the coverage accuracy of bootstrap confidence intervals for impulse response estimates which are closely related with multi-step-ahead prediction intervals. In this paper, we propose different ways of introducing the model selection step in the resampling algorithm. We present a Monte Carlo study comparing the finite sample properties of the proposed method with those of alternative methods in the case of prediction intervals.