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Time-varying copula models for financial time series

Part of: Nonparametric inference Mathematical economics Inference from stochastic processes

Published online by Cambridge University Press:  25 July 2016

Rüdiger Kiesel ,
Magda Mroz  and
Ulrich Stadtmüller
Rüdiger Kiesel*
Affiliation:
University of Duisburg-Essen
Magda Mroz*
Affiliation:
Ulm University
Ulrich Stadtmüller*
Affiliation:
Ulm University
*
Chair for Energy Trading and Finance, University of Duisburg-Essen, Campus Essen, Universitätsstraße 12, 45141 Essen, Germany. Email address: ruediger.kiesel@uni-due.de
Institut für Zahlentheorie und Wahrscheinlichkeitstheorie, Ulm University, 89069 Ulm, Germany. Email address: magda.mroz@web.de
Institut für Zahlentheorie und Wahrscheinlichkeitstheorie, Ulm University, 89069 Ulm, Germany. Email address: ulrich.stadtmueller@uni-ulm.de
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Abstract

We perform an analysis of the potential time inhomogeneity in the dependence between multiple financial time series. To this end, we use the framework of copula theory and tackle the question of whether dependencies in such a case can be assumed constant throughout time or rather have to be modeled in a time-inhomogeneous way. We focus on parametric copula models and suitable inference techniques in the context of a special copula-based multivariate time series model. A recent result due to Chan et al. (2009) is used to derive the joint limiting distribution of local maximum-likelihood estimators on overlapping samples. By restricting the overlap to be fixed, we establish the limiting law of the maximum of the estimator series. Based on the limiting distributions, we develop statistical homogeneity tests, and investigate their local power properties. A Monte Carlo simulation study demonstrates that bootstrapped variance estimates are needed in finite samples. Empirical analyses on real-world financial data finally confirm that time-varying parameters are an exception rather than the rule.

Keywords

Multivariate time seriescopulabinomial testextremal test

MSC classification

Primary: 62M10: Time series, auto-correlation, regression, etc.
Secondary: 62G32: Statistics of extreme values; tail inference 91B84: Economic time series analysis
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue A: Probability, Analysis and Number Theory , July 2016 , pp. 159 - 180
Copyright
Copyright © Applied Probability Trust 2016 

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