CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility

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

Abstract

We generalise the Homm and Breitung (2012) CUSUM-based procedure for the real-time detection of explosive autoregressive episodes in financial price data to allow for time-varying volatility. Such behaviour can heavily inflate the false positive rate [FPR] of the CUSUMbased procedure to spuriously signal the presence of an explosive episode. Our modified procedure involves replacing the standard variance estimate in the CUSUM statistics with a nonparametric kernel-based spot variance estimate. We show that the sequence of modified CUSUM statistics has a joint limiting null distribution which is invariant to any time-varying volatility present in the innovations and that this delivers a real-time monitoring procedure whose theoretical FPR is controlled. Simulations show that the modification is effective in controlling the empirical FPR of the procedure, yet sacrifices only a small amount of power to detect explosive episodes, relative to the standard procedure, when the shocks are homoskedastic. An empirical illustration using Bitcoin price data is provided.

Citation

Astill, S., Harvey, D. I., Leybourne, S. J., Taylor, A. R., & Zu, Y. (2023). CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility. Journal of Financial Econometrics, 21(1), 187-227. https://doi.org/10.1093/jjfinec/nbab009

• Journal Article Type: Article
• Acceptance Date: Mar 12, 2021
• Online Publication Date: May 5, 2021
• Publication Date: 2023-01
• Deposit Date: Mar 15, 2021
• Publicly Available Date: May 6, 2023
• Journal: Journal of Financial Econometrics
• Print ISSN: 1479-8409
• Electronic ISSN: 1479-8417
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 21
• Issue: 1
• Pages: 187-227
• DOI: https://doi.org/10.1093/jjfinec/nbab009
• Keywords: Economics and Econometrics; Finance
• Public URL: https://nottingham-repository.worktribe.com/output/5396026
• Publisher URL: https://academic.oup.com/jfec/advance-article/doi/10.1093/jjfinec/nbab009/6268988