Geodesic
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

Voir la notice de l'article provenant de la source Numdam

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.

DOI : 10.1051/ps/2011158
Classification : 60E07, 60G10, 28D10, 91G70
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},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2011158},
     mrnumber = {3070886},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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  - http://geodesic.mathdoc.fr/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 http://geodesic.mathdoc.fr/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

Cité par Sources :