Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model

Fuchs, Florian; Stelzer, Robert

ESAIM: Probability and Statistics, Tome 17 (2013), pp. 455-471.

We consider strictly stationary infinitely divisible processes and first extend the mixing conditions given in Maruyama [Theory Probab. Appl. 15 (1970) 1-22] and Rosiński and Żak [Stoc. Proc. Appl. 61 (1996) 277-288] from the univariate to the d-dimensional case. Thereafter, we show that multivariate Lévy-driven mixed moving average processes satisfy these conditions and hence a wide range of well-known processes such as superpositions of Ornstein - Uhlenbeck (supOU) processes or (fractionally integrated) continuous time autoregressive moving average (CARMA) processes are always mixing. Finally, mixing of the log-returns and the integrated volatility process of a multivariate supOU type stochastic volatility model, recently introduced in Barndorff - Nielsen and Stelzer [Math. Finance 23 (2013) 275-296], is established.

Classification : 60E07, 60G10, 28D10, 91G70
Mots clés : infinitely divisible process, mixing, mixed moving average process, supOU process, stochastic volatility model, codifference

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