AI 中文总结
研究重尾移动平均中长记忆与突变原理的相互作用，通过分析双无穷移动平均过程，发现长记忆使更多突变起作用，导致更长且性质不同的聚类模式。
AI 中文摘要
平稳随机过程中大幅偏差事件的聚类严重依赖于边际分布的尾部行为与时间依赖性强度之间的相互作用。在双无穷移动平均过程类中，当记忆短时，先前工作已分别在轻尾和重尾情形下的聚类模式间建立了鲜明对比，分别由“共谋”和“突变”原理主导。还描述了长记忆如何与共谋原理相互作用以影响轻尾情形下的聚类。本文探讨重尾情形下长记忆与突变原理的相互作用。结果表明，长记忆通常允许更广泛的突变发挥作用，并导致更长且性质不同的聚类模式。
英文摘要
Clustering of large deviations events in a stationary stochastic process depends critically on the interplay between the tail behavior of the marginal distribution and the strength of temporal dependence. In the class of doubly infinite moving average processes, when the memory is short, previous work has established a sharp contrast in the clustering patterns between light- and heavy-tailed settings, governed by \textit{conspiracy} and \textit{catastrophe} principles respectively. It has also been described how long memory interacts with the conspiracy principle to affect clustering in the light-tailed case. This paper addresses the interaction of long memory with the catastrophe principle in the heavy-tailed case. It turns out that long memory generally allows for a wider range of catastrophes to play a role and leads to longer and qualitatively different clustering patterns.
