Tail behavior of multivariate lévy-driven mixed moving average processes and supOU Stochastic Volatility Models

Martin Moser, Robert Stelzer
2011 Advances in Applied Probability  
Multivariate Lévy-driven mixed moving average (MMA) processes of the type X t = ∬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
more » ... e 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.
doi:10.1017/s0001867800005322 fatcat:m6dskmzwrjgqhjtpicyckw6wua