Empirical Characteristic Functions‐Based Estimation and Distance Correlation for Locally Stationary Processes. (14th August 2019)

• Record Type: Journal Article
• Authors: Jentsch, Carsten; Leucht, Anne; Meyer, Marco; Beering, Carina
• Is Part Of: Journal of time series analysis. Volume 41:Number 1(2020)
• Page Start: 110
• Page End: 133
• Publication Date: 2019-08-14
• Subjects: Empirical characteristic function -- local stationarity -- α‐stable distributions -- distance correlation -- minimum distance estimation -- asymptotic theory; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12497
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract : In this article, 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 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.