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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

Authors

YANG ZU yang.zu@nottingham.ac.uk
Assistant Professor



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.

Journal Article Type Article
Publication Date 2019-01
Print ISSN 0266-4666
Publisher Cambridge University Press (CUP)
Peer Reviewed Peer Reviewed
APA6 Citation Harvey, D. I., Leybourne, S. J., & Zu, Y. (2019). Sign-based Unit Root Tests for Explosive Financial Bubbles in the Presence of Deterministically Time-Varying Volatility. Econometric Theory,
Keywords Rational bubble; Explosive autoregression; Time-varying volatility; Right-tailed unit root testing; Sign-based test JEL Classi…cation: C12, C32
Additional Information This article will be published in a revised form in Econometric Theory https://www.cambridge.o...als/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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