Title: Empirical characteristic function-based inference for locally stationary processes
Authors: Marco Meyer - TU Braunschweig (Germany) [presenting]
Carsten Jentsch - TU Dortmund University (Germany)
Anne Leucht - Technische Universitat Braunschweig (Germany)
Carina Beering - TU Braunschweig (Germany)
Abstract: A kernel-type estimator is proposed for the local characteristic function (local CF) of locally stationary processes. Under weak moment conditions, we prove joint asymptotic normality for local empirical characteristic functions (local ECF). Precisely, for processes having a (two-sided) time-varying MA($\infty$) representation, we establish a central limit theorem under the assumption of finite absolute first moments of the process. Additionally, we prove process convergence of the local ECF. We apply our asymptotic results to parameter estimation of time-varying $\alpha$-stable distributions. Furthermore, we extend the notion of distance correlation to locally stationary processes and provide asymptotic theory for local empirical distance correlations. Finally, we provide a simulation study on minimum distance estimation for $\alpha$-stable distributions based on local ECF and illustrate the pairwise dependence structure over time of log returns of German stock prices via local empirical distance correlations.