Adaptive wild bootstrap tests for a unit root with non-stationary volatility

Boswijk, Peter; Zu, Yang

Abstract

© 2017 The Authors. The Econometrics Journal published by John Wiley & Sons Ltd on behalf of Royal Economic Society. Recent research has emphasized that permanent changes in the innovation variance (caused by structural shifts or an integrated volatility process) lead to size distortions in conventional unit root tests. It has been shown how these size distortions can be resolved using the wild bootstrap. In this paper, we first derive the asymptotic power envelope for the unit root testing problem when the non-stationary volatility process is known. Next, we show that under suitable conditions, adaptation with respect to the volatility process is possible, in the sense that non-parametric estimation of the volatility process leads to the same asymptotic power envelope. Implementation of the resulting test involves cross-validation and the wild bootstrap. A Monte Carlo experiment shows that the asymptotic results are reflected in finite sample properties, and an empirical analysis of real exchange rates illustrates the applicability of the proposed procedures.

Citation

Boswijk, P., & Zu, Y. (2018). Adaptive wild bootstrap tests for a unit root with non-stationary volatility. Econometrics Journal, 21(2), 87-113. https://doi.org/10.1111/ectj.12100

• Journal Article Type: Article
• Acceptance Date: Jul 25, 2017
• Online Publication Date: Jan 16, 2018
• Publication Date: Jun 29, 2018
• Deposit Date: Sep 13, 2017
• Publicly Available Date: Jan 16, 2018
• Journal: Econometrics Journal
• Print ISSN: 1368-4221
• Electronic ISSN: 1368-423X
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 2
• Pages: 87-113
• DOI: https://doi.org/10.1111/ectj.12100
• Keywords: Unit root, Adaptive testing, Nonparametric estimation, Power envelope, Wild boot-strap
• Public URL: https://nottingham-repository.worktribe.com/output/905683
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1111/ectj.12100/abstract