Bootstrapping Nonstationary Autoregressive Processes with Predictive Regression Models

TL;DR

This paper proves the asymptotic validity of a bootstrap-based estimator for predictive regression models with nearly nonstationary autoregressive processes, supported by theoretical analysis and Monte Carlo simulations.

Contribution

It establishes the asymptotic validity of the bootstrap IVX estimator for local-to-unity autoregressive models, covering both nearly stationary and nonstationary cases.

Findings

Bootstrap IVX estimator has a mixed Gaussian limit distribution.

Theoretical results are supported by Monte Carlo experiments.

Estimator is valid for a wide range of local-to-unity processes.

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.