Max-semistable extreme value laws for autoregressive processes with Cantor-like marginals

2024/08/30 by Alef Sterk, Sterk, Alef E. · 1 citation
Economics, Econometrics and Finance · #60F99 #60G70 #Dynamical Systems (math.DS) #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2408.17058

openalex publication_date 2024/08/30 · openalex created_date 2024/10/19 · openalex updated_date 2026/07/28

Abstract

This paper considers a family of autoregressive processes with marginal distributions resembling the Cantor function. It is shown that the marginal distribution is in the domain of attraction of a max-semistable distribution. The main result is that the extreme value law for the autoregressive process is obtained by including an extremal index in the law for an i.i.d. process with the same marginal distribution. Connections with extremes in deterministic dynamical systems and the relevance of max-semistable distributions in that context are also pointed out.

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