Intermittency and infinite variance: the case of integrated supOU processes

2019/03/29 by Danijel Grahovac, Nikolai Leonenko, Nikolai N. Leonenko +4
Economics, Econometrics and Finance · Mathematics · #60F05 #60G10 #60G52 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #math.PR #msc:60F05 #msc:60G10 #msc:60G52

paper · pdf · doi:10.48550/arxiv.1904.00100

openalex publication_date 2019/03/29 · arxiv created 2021/03/17 · arxiv updated 2021/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence structure can be specified independently. Integrated supOU processes have then stationary increments and satisfy central and non-central limit theorems. Their moments, however, can display an unusual behavior known as "intermittency". We show here that intermittency can also appear when the processes have a heavy tailed marginal distribution and, in particular, an infinite variance.

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