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Empirical Characteristic Functions‐Based Estimation and Distance Correlation for Locally Stationary Processes
Author(s) -
Jentsch Carsten,
Leucht Anne,
Meyer Marco,
Beering Carina
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12497
Subject(s) - mathematics , estimator , central limit theorem , weak convergence , asymptotic distribution , pairwise comparison , mathematical analysis , statistics , computer security , computer science , asset (computer security)
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.