منابع مشابه
Spectral Representation of Multivariate Regularly Varying Lévy and CARMA Processes
A spectral representation for regularly varying Lévy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail giving also new insight in the L2-case where the noise is a random orthogonal measure. This allows a spectral definition of multivariate regularly varying Lévy-driven continuous time autoregressive moving average (C...
متن کاملParametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations
We consider the parametric estimation of the driving Lévy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid (0, h, 2h, . . .). Beginning with a new state space representation, we develop a method to recover the driving Lévy process exactly from a continuous record of the observed MCARMA process. We use tools fro...
متن کاملQuasi maximum likelihood estimation for strongly mixing state space models and multivariate Lévy-driven CARMA processes
We consider quasi maximum likelihood (QML) estimation for general non-Gaussian discrete-time linear state space models and equidistantly observed multivariate Lévy-driven continuous-time autoregressive moving average (MCARMA) processes. In the discrete-time setting, we prove strong consistency and asymptotic normality of the QML estimator under standard moment assumptions and a strong-mixing co...
متن کاملMultivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes
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...
متن کاملCARMA processes as solutions of integral equations
A CARMA(p, q) process is defined by suitable interpretation of the formal p order differential equation a(D)Yt = b(D)DLt, where L is a two-sided Lévy process, a(z) and b(z) are polynomials of degrees p and q, respectively, with p > q, and D denotes the differentiation operator. Since derivatives of Lévy processes do not exist in the usual sense, the rigorous definition of a CARMA process is bas...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2007
ISSN: 0304-4149
DOI: 10.1016/j.spa.2006.05.014