 Clustering of large deviations events in heavy-tailed moving average processes: The catastrophe principle in the short-memory caseJiaqi Wang and Gennady Samorodnitsky Stochastic Processes and their Applications, 2026, vol. 193, issue C Abstract: How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the process. In this paper we work in the context of large deviations for partial sums in moving average processes with short memory and regularly varying tails. We show that the structure of the large deviation cluster in this case markedly differs from the corresponding structure in the case of exponentially light tails, considered in Chakrabarty and Samorodnitsky (2024). This is due to the difference between the “conspiracy” vs. the “catastrophe” principles underlying the large deviation events in the light tailed case and the heavy tailed case, correspondingly. Keywords: Large deviations; Clustering; Infinite moving average; Heavy tails; Short memory; Catastrophe principle (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:193:y:2026:i:c:s0304414925002947 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2025.104850 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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