Time-varying Lévy-driven state space models, locally stationary approximations and asymptotic normality

We first introduce time-varying Lévy-driven state space models, as a class of time series models in continuous time encompassing continuous-time autoregressive moving average processes with parameters changing over time.
In order to allow for their statistical analysis we define a notion of locally stationary approximations for sequences of continuous time processes and establish laws of large numbers and central limit type results under \theta-weak dependence assumptions. Finally, we consider the asymptotic behaviour of the empirical mean and autocovariance function of time-varying Lévy-driven state space models under appropriate conditions.
This talk is based on:
Bitter, A., Stelzer, R., Ströh, B. (2023):
Continuous-time Locally Stationary Time Series Models
Advances in Applied Probability, 55 no. 3, 965 - 99
Stelzer, R., Ströh, B. (2022):
Asymptotics of Time-varying Processes in Continuous-Time using Locally Stationary Approximations
arXiv:2105.00223

Seminar organized by Prof. Hashorva