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

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