Publications
4 results found
Stroh B, Curato IV, Stelzer R, 2021, Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields, Annals of Applied Probability, ISSN: 1050-5164
Stroh B, 2021, Statistical inference for continuous-time locally stationary processes using stationary approximations
Statistical inference for continuous-time locally stationary processes using stationary approximations
Stroh B, Stelzer R, 2021, Approximations and asymptotics of continuous-time locally stationary processes
We introduce a general theory on stationary approximations for locally stationary contin- uous-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 transforma- tions 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.
Stroh B, Bitter A, Stelzer R, 2021, Continuous-time locally stationary time series models
We adapt the classical definition of locally stationary processes in discrete-time to the continuous-time setting and obtain equivalent representations in the time and frequency domain. From this, a unique time-varying spectral density is derived using the Wigner-Ville spectrum. As an example, we investigate time-varying Lévy-driven state space processes, including the class of time-varying Lévy-driven CARMA processes. First, the connection between these two classes of processes is examined. Considering a sequence of time-varying Lévy-driven state space processes, we then give sufficient conditions on the coefficient functions that ensure local stationarity with respect to the given definition.
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.