A large deviations approach to limit theory for heavy-tailed time series

• 成果类型: Article
• 署名作者: Mikosch, Thomas; Wintenberger, Olivier
• 署名单位: University of Copenhagen; Sorbonne Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0654-4
• 发表日期: 2016
• 页码: 233-269
• 关键词: alpha-stable domain; Moving averages; point-processes; minimal conditions; Regular Variation; random-variables; CONVERGENCE; distributions; sums; stationary

摘要

In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin. We study a variety of such functionals, including large deviations of random walks, their suprema, the ruin functional, and further derive weak limit theory for maxima, point processes, cluster functionals and the tail empirical process. One of the main results of this paper concerns bounds for the ruin probability in various heavy-tailed models including GARCH, stochastic volatility models and solutions to stochastic recurrence equations.