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SIGN-BASED UNIT ROOT TESTS FOR EXPLOSIVE FINANCIAL BUBBLES IN THE PRESENCE OF DETERMINISTICALLY TIME-VARYING VOLATILITY

Published online by Cambridge University Press:  29 March 2019

David I. Harvey ,
Stephen J. Leybourne  and
Yang Zu
David I. Harvey*
Affiliation:
University of Nottingham
Stephen J. Leybourne
Affiliation:
University of Nottingham
Yang Zu
Affiliation:
University of Nottingham
*
*Address correspondence to David Harvey, School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK; e-mail: dave.harvey@nottingham.ac.uk.
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Abstract

This article considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a sign-based variant of the Phillips, Shi, and Yu (2015, International Economic Review 56, 1043–1077) 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 specifications. However, since the original test can still outperform the sign-based one for some specifications, 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.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 1 , February 2020 , pp. 122 - 169
Copyright
Copyright © Cambridge University Press 2019 

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Footnotes

We are grateful to the Editor, Peter Phillips, the Co-Editor, Anna Mikusheva, and three anonymous referees for their very helpful and constructive comments.

References

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