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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


Professor of Econometrics

Associate Professor


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.


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.

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
Keywords Rational bubble; Explosive autoregression; Time-varying volatility; Right-tailed unit root testing; Sign-based test JEL Classi…cation: C12, C32
Public URL
Publisher URL
Additional Information This article will be published in a revised form in 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


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