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Tests for an end-of-sample bubble in financial time series

Astill, Sam; Harvey, David I.; Leybourne, Stephen J.; Taylor, Robert

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Sam Astill

Professor of Econometrics

Robert Taylor


In this paper we examine the issue of detecting explosive behaviour in economic and financial time series when an explosive episode is both ongoing at the end of the sample, and of finite length. We propose a testing strategy based on the sub-sampling method of Andrews (2003), in which a suitable test statistic is calculated on a finite number of end-of-sample observations, with a critical value obtained using sub-sample test statistics calculated on the remaining observations. This approach also has the practical advantage that, by virtue of how the critical values are obtained, it can deliver tests which are robust to, among other things, conditional heteroskedasticity and serial correlation in the driving shocks. We also explore modifications of the raw statistics to account for unconditional heteroskedasticity using studentisation and a White-type correction. We evaluate the finite sample size and power properties of our proposed procedures, and find that they offer promising levels of power, suggesting the possibility for earlier detection of end-of-sample bubble episodes compared to existing procedures.

Journal Article Type Article
Acceptance Date Oct 3, 2016
Online Publication Date Mar 22, 2017
Deposit Date Oct 21, 2016
Publicly Available Date Mar 22, 2017
Journal Econometric Reviews
Print ISSN 0747-4938
Electronic ISSN 1532-4168
Publisher Taylor & Francis Open
Peer Reviewed Peer Reviewed
Volume 36
Issue 6-9
Keywords Rational bubble; Explosive autoregression; Right-tailed unit root testing: Sub-sampling
Public URL
Publisher URL
Additional Information “This is an Accepted Manuscript of an article published by Taylor & Francis in Econometric Reviews on 22 March 2017, available online:


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