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

Sam Astill, David I Harvey, Stephen J Leybourne, Robert Taylor and Yang Zu

Journal of Financial Econometrics, 2023, vol. 21, issue 1, 187-227

Abstract: We generalize 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 behavior can heavily inflate the false positive rate (FPR) of the CUSUM-based 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.

Keywords: CUSUM; explosive autoregression; nonparametric spot volatility estimator; rational bubble; real-time monitoring (search for similar items in EconPapers)
JEL-codes: C12 C22 G14 (search for similar items in EconPapers)
Date: 2023
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