arXiv subjects

Bennet Ströh

Publications and source records attributed to Bennet Ströh.

4 recordsLinked to original sources

arXiv2022

Asymptotics of time-varying processes in continuous-time using locally stationary approximations

We introduce a general theory on stationary approximations for locally stationary continuous-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 transformations 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.

math.PR↗

arXiv2021

Statistical inference for continuous-time locally stationary processes using stationary approximations

We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $θ$-weak dependence, and hereditary properties, we give sufficient conditions on the contrast function that ensure consistency and asymptotic normality of the $M$-estimator. As an example, we obtain consistency and asymptotic normality of a localized least squares estimator for observations from a sequence of time-varying Lévy-driven Ornstein-Uhlenbeck processes. Furthermore, for a sequence of time-varying Lévy-driven state space models, we show consistency of a localized Whittle estimator and an $M$-estimator that is based on a quasi maximum likelihood contrast. Simulation studies show the applicability of the estimation procedures.

math.ST↗

arXiv2021

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.

math.PR↗

arXiv2021

Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields

We obtain central limit theorems for stationary random fields employing a novel measure of dependence called $θ$-lex weak dependence. We show that this dependence notion is more general than strong mixing, i.e., it applies to a broader class of models. Moreover, we discuss hereditary properties for $θ$-lex and $η$-weak dependence and illustrate the possible applications of the weak dependence notions to the study of the asymptotic properties of stationary random fields. Our general results apply to mixed moving average fields (MMAF in short) and ambit fields. We show general conditions such that MMAF and ambit fields, with the volatility field being an MMAF or a $p$-dependent random field, are weakly dependent. For all the models mentioned above, we give a complete characterization of their weak dependence coefficients and sufficient conditions to obtain the asymptotic normality of their sample moments. Finally, we give explicit computations of the weak dependence coefficients of MSTOU processes and analyze under which conditions the developed asymptotic theory applies to CARMA fields.

math.ST↗