Department of Economics
University of Mannheim, Germany
Empirical Characteristic Functions-Based Estimation and Distance Correlation for Locally Stationary Processes
In this paper, we propose a kernel-type estimator 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(∞ 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 distributions. Furthermore, by extending the notion of distance correlation of Szekely et al. (2007) to locally stationary processes, we are able to provide asymptotic theory for local empirical distance correlations. Finally, we provide a simulation study on minimum distance estimation for α-stable distributions and illustrate the pairwise dependence structure over time of log returns of German stock prices via local empirical distance correlations.
Joint work with Carina Beering, Anne Leucht and Marco Meyer.