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Tests for explosive financial bubbles in the presence of non-stationary volatility

Harvey, David I.; Leybourne, Stephen J.; Sollis, Robert; Taylor, A.M. Robert

Authors

Robert Sollis

A.M. Robert Taylor



Abstract

This paper studies the impact of permanent volatility shifts in the innovation process on the performance of the test for explosive financial bubbles based on recursive right-tailed Dickey–Fuller-type unit root tests proposed by Phillips, Wu and Yu (2011). We show that, in this situation, their supremum-based test has a non-pivotal limit distribution under the unit root null, and can be quite severely over-sized, thereby giving rise to spurious indications of explosive behaviour. We investigate the performance of a wild bootstrap implementation of their test procedure for this problem, and show it is effective in controlling size, both asymptotically and in finite samples, yet does not sacrifice power relative to an (infeasible) size-adjusted version of their test, even when the shocks are homoskedastic. We also discuss an empirical application involving commodity price time series and find considerably less emphatic evidence for the presence of explosive bubbles in these data when using our proposed wild bootstrap implementation of the Phillips, Wu and Yu (2011) test.

Journal Article Type Article
Journal Journal of Empirical Finance
Print ISSN 0927-5398
Electronic ISSN 1879-1727
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 38
Issue B
APA6 Citation Harvey, D. I., Leybourne, S. J., Sollis, R., & Taylor, A. R. (in press). Tests for explosive financial bubbles in the presence of non-stationary volatility. Journal of Empirical Finance, 38(B), https://doi.org/10.1016/j.jempfin.2015.09.002
DOI https://doi.org/10.1016/j.jempfin.2015.09.002
Keywords Rational bubble; Explosive autoregression; Non-stationary volatility; Right-tailed unit root testing
Publisher URL http://www.sciencedirect.com/science/article/pii/S0927539815000961
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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