Sign-based Unit Root Tests for Explosive Financial Bubbles in the Presence of Deterministically Time-Varying Volatility

Harvey, David I.; Leybourne, Stephen J.; Zu, Yang

Abstract

This paper considers the problem of testing for an explosive bubble in …nancial data in the presence of time-varying volatility. We propose a sign-based variant of the Phillips, Shi and Yu (2015) test. Unlike the original test, the sign-based test does not require bootstrap-type methods to control size in the presence of time-varying volatility. Under a locally explosive alternative, the sign-based test delivers higher power than the original test for many time-varying volatility and bubble speci…cations. However, since the original test can still outperform the sign-based one for some speci…cations, we also propose a union of rejections procedure that combines the original and sign-based tests, employing a wild bootstrap to control size. This is shown to capture most of the power available from the better performing of the two tests. We also show how a sign-based statistic can be used to date the bubble start and end points. An empirical illustration using Bitcoin price data is provided.

Citation

Harvey, D. I., Leybourne, S. J., & Zu, Y. (2020). Sign-based Unit Root Tests for Explosive Financial Bubbles in the Presence of Deterministically Time-Varying Volatility. Econometric Theory, 36(1), 122-169. https://doi.org/10.1017/S0266466619000057

• Journal Article Type: Article
• Acceptance Date: Jan 10, 2019
• Online Publication Date: Mar 29, 2019
• Publication Date: 2020-02
• Deposit Date: Jan 14, 2019
• Publicly Available Date: Jan 14, 2019
• Journal: Econometric Theory
• Print ISSN: 0266-4666
• Electronic ISSN: 1469-4360
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 36
• Issue: 1
• Pages: 122-169
• DOI: https://doi.org/10.1017/S0266466619000057
• Keywords: Rational bubble; Explosive autoregression; Time-varying volatility; Right-tailed unit root testing; Sign-based test JEL Classi…cation: C12, C32
• Public URL: https://nottingham-repository.worktribe.com/output/1466899
• Publisher URL: https://www.cambridge.org/core/journals/econometric-theory/article/abs/signbased-unit-root-tests-for-explosive-financial-bubbles-in-the-presence-of-deterministically-timevarying-volatility/1B3CDC63DCBDD48066776016DA7850CD
• Additional Information: This article will be published in a revised form in Econometric Theory https://www.cambridge.org/core/journals/econometric-theory. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder
• Contract Date: Jan 14, 2019