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.
Keywords: infinitely divisible process, mixing, mixed moving average process, supOU process, stochastic volatility model, codifference
@article{PS_2013__17__455_0,
author = {Fuchs, Florian and Stelzer, Robert},
title = {Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the {supOU} stochastic volatility model},
journal = {ESAIM: Probability and Statistics},
pages = {455--471},
year = {2013},
publisher = {EDP Sciences},
volume = {17},
doi = {10.1051/ps/2011158},
mrnumber = {3070886},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2011158/}
}
TY - JOUR AU - Fuchs, Florian AU - Stelzer, Robert TI - Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model JO - ESAIM: Probability and Statistics PY - 2013 SP - 455 EP - 471 VL - 17 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps/2011158/ DO - 10.1051/ps/2011158 LA - en ID - PS_2013__17__455_0 ER -
%0 Journal Article %A Fuchs, Florian %A Stelzer, Robert %T Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model %J ESAIM: Probability and Statistics %D 2013 %P 455-471 %V 17 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps/2011158/ %R 10.1051/ps/2011158 %G en %F PS_2013__17__455_0
Fuchs, Florian; Stelzer, Robert. Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 455-471. doi: 10.1051/ps/2011158
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