Continuous-time locally stationary time series models

2021/04/28 by Annemarie Bitter, Bitter, Annemarie, Robert Stelzer +3
Engineering · #60G51 #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Probability (math.PR) #Statistics Theory (math.ST) #primary 60G07 #secondary 62M15

paper · pdf · doi:10.48550/arxiv.2104.13796

openalex publication_date 2021/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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.

Related

• Locally Stationary Processes
• Asymptotics of time-varying processes in continuous-time using locally stationary approximations
• On Locally Dyadic Stationary Processes
• Spectral Representation of Multivariate Regularly Varying Lévy and CARMA processes
• Statistical inference for continuous-time locally stationary processes using stationary approximations