Bootstrapping Nonstationary Autoregressive Processes with Predictive Regression Models

Abstract

We establish the asymptotic validity of the bootstrap-based IVX estimator proposed by Phillips and Magdalinos (2009) for the predictive regression model parameter based on a local-to-unity specification of the autoregressive coefficient which covers both nearly nonstationary and nearly stationary processes. A mixed Gaussian limit distribution is obtained for the bootstrap-based IVX estimator. The statistical validity of the theoretical results are illustrated by Monte Carlo experiments for various statistical inference problems.