CUSUM-Based Monitoring for Explosive Episodes in Financial Data in the Presence of Time-Varying Volatility
针对金融价格数据中爆发性自回归阶段的实时检测，改进了CUSUM方法以允许时变波动率，使用非参数核估计的瞬时方差替代标准方差估计，控制误报率并保持检测效力，并用比特币数据验证。
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.