Continuous-time locally stationary time series models

Abstract We adapt the classical definition of locally stationary processes in discrete time (see e.g. Dahlhaus, ‘Locally processes’, Time Series Analysis: Methods and Applications (2012)) to continuous-time setting obtain equivalent representations frequency domains. From this, a unique time-varying spectral density is derived using Wigner–Ville spectrum. As an example, we investigate Lévy-driven state space processes, including class CARMA processes. First, connection between these two classes examined. Considering sequence then give sufficient conditions on coefficient functions that ensure local stationarity with respect given definition.