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.

中文翻译：

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基于 CUSUM 的金融数据爆炸性事件监测在时变波动的情况下

我们推广了 Homm 和 Breitung (2012) 基于 CUSUM 的程序，用于实时检测金融价格数据中的爆炸性自回归事件，以允许随时间变化的波动。这种行为会严重夸大基于 CUSUM 的过程的误报率 (FPR)，以虚假地发出爆炸性事件存在的信号。我们修改过的程序包括用基于非参数核的点方差估计替换 CUSUM 统计中的标准方差估计。我们表明，修改后的 CUSUM 统计序列具有联合限制零分布，该分布对于创新中存在的任何时变波动性都是不变的，并且这提供了一个实时监控过程，其理论 FPR 受到控制。模拟表明，修改在控制过程的经验 FPR 方面是有效的，但相对于标准过程，当冲击是同方差的时，只牺牲少量的功率来检测爆炸事件。提供了使用比特币价格数据的经验说明。