Bernoulli

Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes

Eckhard Schlemm and Robert Stelzer

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Abstract

The class of multivariate Lévy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of continuous-time state space models. The linear innovations of the weak ARMA process arising from sampling an MCARMA process at an equidistant grid are proved to be exponentially completely regular (β-mixing) under a mild continuity assumption on the driving Lévy process. It is verified that this continuity assumption is satisfied in most practically relevant situations, including the case where the driving Lévy process has a non-singular Gaussian component, is compound Poisson with an absolutely continuous jump size distribution or has an infinite Lévy measure admitting a density around zero.

Article information

Source
Bernoulli, Volume 18, Number 1 (2012), 46-63.

Dates
First available in Project Euclid: 20 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.bj/1327068617

Digital Object Identifier
doi:10.3150/10-BEJ329

Mathematical Reviews number (MathSciNet)
MR2888698

Zentralblatt MATH identifier
1248.60039

Keywords
complete regularity linear innovations multivariate CARMA process sampling state space representation strong mixing vector ARMA process

Citation

Schlemm, Eckhard; Stelzer, Robert. Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes. Bernoulli 18 (2012), no. 1, 46--63. doi:10.3150/10-BEJ329. https://projecteuclid.org/euclid.bj/1327068617


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