Abstract
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.
Citation
Martin Moser. Robert Stelzer. "Tail behavior of multivariate Lévy-driven mixed moving average processes and supOU stochastic volatility models." Adv. in Appl. Probab. 43 (4) 1109 - 1135, Decemmber 2011. https://doi.org/10.1239/aap/1324045701
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