CARMA processes

Introductary talk to continuous-time locally stationary processes.

We establish asymptotic properties of M-estimator based on observations from a continuous-time locally stationary process. Simulation studies show the applicability of the estimation procedures.

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use θ-weak dependence to establish laws of large numbers and central limit type results under different observation schemes.

We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting. As an example, we investigate time-varying Lévy-driven state space processes, including the class of time-varying Lévy-driven CARMA processes.