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Real-time monitoring for explosive financial bubbles

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


Sam Astill

Professor of Econometrics

Robert Sollis

A.M. Robert Taylor


We propose new methods for the real-time detection of explosive bubbles in financial time series. Most extant methods are constructed for a fixed sample of data and, as such, are only appropriate when applied as one-shot tests. Sequential application of these, declaring the presence of a bubble as soon as one of these statistics exceeds the one-shot critical value, would yield a detection procedure with an unknown false positive rate likely to be far in excess of the nominal level. Our approach sequentially applies the one-shot tests of Astill et al. (2017), comparing sub-sample statistics calculated in real time during the monitoring period with corresponding sub-sample statistics obtained from a prior training period. We propose two procedures: one based on comparing the real time monitoring period statistics with the maximum statistic over the training period, and another which compares the number of consecutive exceedances of a threshold value in the monitoring and training periods, the threshold value obtained from the training period. Both allow the practitioner to determine the false positive rate for any given monitoring horizon, or to ensure this rate does not exceed a specified level by setting a maximum monitoring horizon. Monte Carlo simulations suggest that the finite sample false positive rates lie close to their theoretical counterparts, even in the presence of time-varying volatility and serial correlation in the shocks. The procedures are shown to perform well in the presence of a bubble in the monitoring period, offering the possibility of rapid detection of an emerging bubble in a real time setting. An empirical application to monthly stock market index data is considered.

Journal Article Type Article
Acceptance Date May 30, 2018
Online Publication Date Jul 19, 2018
Publication Date Nov 30, 2018
Deposit Date Jun 6, 2018
Publicly Available Date Jul 20, 2019
Journal Journal of Time Series Analysis
Print ISSN 0143-9782
Electronic ISSN 1467-9892
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 39
Issue 6
Pages 863-891
Keywords Rational bubble; Explosive autoregression; Real-time monitoring procedure; Subsampling
Public URL
Publisher URL
Additional Information This is the peer reviewed version of the following article: Astill, S. , Harvey, D. I., Leybourne, S. J., Sollis, R. and Robert Taylor, A. M. (2018), Real‐Time Monitoring for Explosive Financial Bubbles. J. Time Ser. Anal., 39: 863-891. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.


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