CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility. (5th May 2021)

• Record Type: Journal Article
• Authors: Astill, Sam; Harvey, David I; Leybourne, Stephen J; Taylor, A M Robert; Zu, Yang
• Is Part Of: Journal of financial econometrics. Volume 21:Number 1(2023)
• Page Start: 187
• Page End: 227
• Publication Date: 2021-05-05
• Subjects: CUSUM -- explosive autoregression -- nonparametric spot volatility estimator -- rational bubble -- real-time monitoring; C22 -- C12 -- G14; Capital market -- Law and legislation -- Periodicals; Financial institutions -- Law and legislation -- Periodicals; 338.544205
• DOI: 10.1093/jjfinec/nbab009
• Languages: English
• ISSNs: 1479-8409

Abstract

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.