Statistica Sinica 14(2004), 155-174

INTRODUCING MODEL UNCERTAINTY

IN TIME SERIES BOOTSTRAP

Andrés M. Alonso$^1$, Daniel Peña$^2$ and Juan Romo$^2$

$^1$Universidad Autonóma de Madrid and $^2$Universidad Carlos III de Madrid

Abstract: It is common in a parametric bootstrap to select the model from the data, and then treat it as it were the true model. Kilian (1998) illustrates 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.

Key words and phrases: Model uncertainty, prediction, sieve bootstrap, time series.