Sequential monitoring for explosive volatility regimes
爆炸性波动率状态的序贯监测AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要聚焦 GARCH 波动率状态的变点监测，并应用于个股日收益。
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爆炸性波动率状态的序贯监测
- 研究问题
- 如何在未知历史及后续波动率状态的情况下，及时发现 GARCH 序列从平稳转向爆炸或反向转变的结构变化？
- 方法与思路
- 作者以对数似然的准 Fisher 得分构造 CUSUM 检测器，并设置较轻权重及 Rényi 权重边界以缩短不同变点的检测延迟。
- 材料陈述的贡献
- 摘要称两类方法无需预先知道状态，并给出检测延迟的极限分布；模拟与个股日收益应用用于检验其表现。
- 阅读关注点
- 核对平稳与爆炸状态下的理论条件、边界校准及误报控制，并比较不同变点位置对应的检测延迟分布和实际表现。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已通过同行评审或被期刊接收；摘要未说明具体正则条件、误报水平与延迟数值。
原文摘要
In this paper, we develop two families of sequential monitoring procedure to (timely) detect changes in a GARCH(1,1) model. Whilst our methodologies can be applied for the general analysis of changepoints in GARCH(1,1) sequences, they are in particular designed to detect changes from stationarity to explosivity or vice versa, thus allowing to check for volatility bubbles. Our statistics can be applied irrespective of whether the historical sample is stationary or not, and indeed without prior knowledge of the regime of the observations before and after the break. In particular, we construct our detectors as the CUSUM process of the quasi-Fisher scores of the log likelihood function. In order to ensure timely detection, we then construct our boundary function (exceeding which would indicate a break) by including a weighting sequence which is designed to shorten the detection delay in the presence of a changepoint. We consider two types of weights: a lighter set of weights, which ensures timely detection in the presence of changes occurring early, but not too early after the end of the historical sample; and a heavier set of weights, called Renyi weights which is designed to ensure timely detection in the presence of changepoints occurring very early in the monitoring horizon. In both cases, we derive the limiting distribution of the detection delays, indicating the expected delay for each set of weights. Our theoretical results are validated via a comprehensive set of simulations, and an empirical application to daily returns of individual stocks.