Empirical characteristic functions-based estimation and distance correlation for locally stationary processes

Jentsch, Carsten ; Leucht, Anne ; Meyer, Marco ; Beering, Carina

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URL: https://ub-madoc.bib.uni-mannheim.de/41438
URN: urn:nbn:de:bsz:180-madoc-414388
Document Type: Working paper
Year of publication: 2016
The title of a journal, publication series: Working Paper Series
Volume: 16-15
Place of publication: Mannheim
Publication language: English
Institution: School of Law and Economics > Statistik (Mammen)
MADOC publication series: Department of Economics > Working Paper Series
Subject: 330 Economics
Classification: MSC: 62G05 , 62G20 , 62M10 , 62H20,
Keywords (English): empirical characteristic function , local stationarity , time series , stable distributions , (local) distance correlation , minimum distance estimation , process convergence , asymptotic theory
Abstract: 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.

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