Jentsch, Carsten Leucht, Anne Meyer, Marco Beering, Carina
Year of Publication:
Working Paper Series 16-15
In this paper, we propose a kernel-type estimator for the local characteristic function of locally stationary processes. Under weak moment conditions, we prove joint asymptotic normality for local empirical characteristic functions. For time-varying linear processes, we establish a central limit theorem under the assumption of finite absolute first moments of the process. Additionally, we prove weak convergence of the local empirical characteristic process. We apply our asymptotic results to parameter estimation. Furthermore, by extending the notion of distance correlation of Szekely, Rizzo and Bakirov (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 a-stable distributions and illustrate the pairwise dependence structure over time of log returns of German stock prices via local empirical distance correlations.
empirical characteristic function local stationarity time series stable distributions (local) distance correlation minimum distance estimation process convergence asymptotic theory