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  • David I. Harvey (a1), Stephen J. Leybourne (a1) and Yang Zu (a1)

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.

Corresponding author
*Address correspondence to David Harvey, School of Economics, University of Nottingham, University Park, Nottingham, NG7 2RD, UK; e-mail:
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We are grateful to the Editor, Peter Phillips, the Co-Editor, Anna Mikusheva, and three anonymous referees for their very helpful and constructive comments.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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