Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 43, Number 4 (2011), 1109-1135.
Tail behavior of multivariate Lévy-driven mixed moving average processes and supOU stochastic volatility models
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.
Adv. in Appl. Probab., Volume 43, Number 4 (2011), 1109-1135.
First available in Project Euclid: 16 December 2011
Permanent link to this document
Digital Object Identifier
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
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. https://projecteuclid.org/euclid.aap/1324045701