CUSUM-based monitoring for explosive episodes in financial data in the presence of time-varying volatility
A CUSUM procedure that detects explosive episodes in financial data in real time while remaining robust to time-varying volatility.
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.
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BibTeX
@article{Astill_2021, title={CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility}, volume={21}, ISSN={1479-8417}, url={http://dx.doi.org/10.1093/jjfinec/nbab009}, DOI={10.1093/jjfinec/nbab009}, number={1}, journal={Journal of Financial Econometrics}, publisher={Oxford University Press (OUP)}, author={Astill, Sam and Harvey, David I and Leybourne, Stephen J and Taylor, A M Robert and Zu, Yang}, year={2021}, month=May, pages={187–227} }