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

Florian Fuchs; Robert Stelzer

ESAIM: Probability and Statistics (2013)

  • Volume: 17, page 455-471
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Fuchs, Florian, and 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 17 (2013): 455-471. <http://eudml.org/doc/273624>.

@article{Fuchs2013,
abstract = {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.},
author = {Fuchs, Florian, Stelzer, Robert},
journal = {ESAIM: Probability and Statistics},
keywords = {infinitely divisible process; mixing; mixed moving average process; supOU process; stochastic volatility model; codifference},
language = {eng},
pages = {455-471},
publisher = {EDP-Sciences},
title = {Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model},
url = {http://eudml.org/doc/273624},
volume = {17},
year = {2013},
}

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
PB - EDP-Sciences
VL - 17
SP - 455
EP - 471
AB - 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.
LA - eng
KW - infinitely divisible process; mixing; mixed moving average process; supOU process; stochastic volatility model; codifference
UR - http://eudml.org/doc/273624
ER -

References

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