Approximations and asymptotics of continuous-time locally stationary processes

Abstract

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. Hereditary properties for a large class of finite and infinite memory transformations show the flexibility of the developed theory. Sufficient conditions for the existence of stationary approximations for time-varying Lévy-driven state space models are derived and compared to existing results. We conclude with comprehensive results on the asymptotic behavior of the first and second order localized sample moments of time-varying Lévy-driven state space models.

Bennet Ströh

Postdoctoral researcher

I am a postdoctoral researcher at the Department of Mathematics at Imperial College London and research associate at the Alan Turing Institute.