Advances in Applied Probability

Tail behavior of multivariate Lévy-driven mixed moving average processes and supOU stochastic volatility models

Martin Moser and Robert Stelzer

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Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∬f(A, t - s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) continuous-time autoregressive moving average processes, and increments of fractional Lévy processes. In this paper we introduce multivariate MMA processes and give conditions for their existence and regular variation of the stationary distributions. Furthermore, we study the tail behavior of multivariate supOU processes and of a stochastic volatility model, where a positive semidefinite supOU process models the stochastic volatility.

Article information

Adv. in Appl. Probab., Volume 43, Number 4 (2011), 1109-1135.

First available in Project Euclid: 16 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes 60G70: Extreme value theory; extremal processes
Secondary: 60H07: Stochastic calculus of variations and the Malliavin calculus 60G10: Stationary processes

Lévy basis mixed moving average process multivariate regular variation supOU process stochastic volatility model tail behavior


Moser, Martin; Stelzer, Robert. Tail behavior of multivariate Lévy-driven mixed moving average processes and supOU stochastic volatility models. Adv. in Appl. Probab. 43 (2011), no. 4, 1109--1135. doi:10.1239/aap/1324045701.

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