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

The class of multivariate Lévy-driven auto-regressive moving-average (MCARMA) processes, the continuous-time analogues 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 Lévy process. It is verified that this continuity assumption is satisfied in most practically relevant situations including the case when 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.     «

The class of multivariate Lévy-driven auto-regressive moving-average (MCARMA) processes, the continuous-time analogues 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 Lévy process. It is verified that t...     »