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Testing for Co-explosive Behaviour in Financial Time Series

Evripidou, Andria C.; Harvey, David I.; Leybourne, Stephen J.; Sollis, Robert

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Andria C. Evripidou

Robert Sollis


This article proposes a test to determine if two price series that each contain an explosive autoregressive regime consistent with the presence of a bubble are related in the sense that a linear combination of them is integrated of order zero. We refer to such a phenomenon as ‘co-explosive behaviour’, and propose a test based on a stationarity testing framework. The test allows the explosive episode in one series to lead (or lag) that in the other by a number of time periods. We establish the asymptotic properties of the test statistic and propose a wild bootstrap procedure for obtaining critical values that are robust to heteroskedasticity. Simulations show that the proposed test has good finite sample size and power performance. An empirical application to detect whether co-explosive behaviour exists among a set of precious and non-ferrous metals is presented.


Evripidou, A. C., Harvey, D. I., Leybourne, S. J., & Sollis, R. (2022). Testing for Co-explosive Behaviour in Financial Time Series. Oxford Bulletin of Economics and Statistics, 84(3), 624-650.

Journal Article Type Article
Acceptance Date Jan 11, 2022
Online Publication Date Mar 9, 2022
Publication Date 2022-06
Deposit Date Feb 11, 2022
Publicly Available Date Mar 9, 2022
Journal Oxford Bulletin of Economics and Statistics
Print ISSN 0305-9049
Electronic ISSN 1468-0084
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 84
Issue 3
Pages 624-650
Keywords Statistics, Probability and Uncertainty; Economics and Econometrics; Social Sciences (miscellaneous); Statistics and Probability
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