Continuous-time locally stationary time series models
Probability
2021-04-29 v1 Statistics Theory
Statistics Theory
Abstract
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 L\'evy-driven state space processes, including the class of time-varying L\'evy-driven CARMA processes. First, the connection between these two classes of processes is examined. Considering a sequence of time-varying L\'evy-driven state space processes, we then give sufficient conditions on the coefficient functions that ensure local stationarity with respect to the given definition.
Cite
@article{arxiv.2104.13796,
title = {Continuous-time locally stationary time series models},
author = {Annemarie Bitter and Robert Stelzer and Bennet Ströh},
journal= {arXiv preprint arXiv:2104.13796},
year = {2021}
}