Volume 17, 2013
|Page(s)||455 - 471|
|Published online||03 June 2013|
Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model
TUM Institute for Advanced Study & Zentrum Mathematik,
Technische Universität München, Boltzmannstraße 3, 85748
2 Institute of Mathematical Finance, Ulm University, Helmholtzstraße 18, 89081 Ulm, Germany
Received: 5 May 2011
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.
Mathematics Subject Classification: 60E07 / 60G10 / 28D10 / 91G70
Key words: Infinitely divisible process / mixing / mixed moving average process / supOU process / stochastic volatility model / codifference
© EDP Sciences, SMAI, 2013
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