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Time-varying copula models for financial time series

Part of: Inference from stochastic processes Nonparametric inference Mathematical economics

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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References

[1] Almeida, C.,Czado, C. and Manner, H. (2012).Modeling high dimensional time-varying dependence using D-vine SCAR models. Preprint. Available at http://arxiv.org/pdf/1202.2008v1.Google Scholar
[2] Bai, J. and Perron, P. (1998).Estimating and testing linear models with multiple structural changes.Econometrica 66,47–78.CrossRefGoogle Scholar
[3] Bentkus, V. (2005).A Lyapunov-type bound in ℝ d .Theory Prob. Appl. 49,311–323.CrossRefGoogle Scholar
[4] Bücher, A.,Kojadinovic, I.,Rohmer, T. and Segers, J. (2014).Detecting changes in cross-sectional dependence in multivariate time series.J. Multivariate Anal. 132,111–128.CrossRefGoogle Scholar
[5] Burger, M.,Graeber, B. and Schindlmayer, G. (2014).Managing Energy Risk: An Integrated View on Power and Other Energy Markets (Wiley Finance Ser. 425),2nd edn.John Wiley,Chichester.CrossRefGoogle Scholar
[6] Chan, N.-H.,Chen, J.,Chen, X.,Fan, Y. and Peng, L. (2009).Statistical inference for multivariate residual copula of GARCH models.Statistica Sinica 19,53–70.Google Scholar
[7] Chen, X. and Fan, Y. (2006).Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification.J. Econometrics 135,125–154.CrossRefGoogle Scholar
[8] Cherubini, U.,Gobbi, F.,Mulinacci, S. and Romagnoli, S. (2010).A copula-based model for spatial and temporal dependence of equity markets. In Copula Theory and Its Applications (Warsaw 2009; Lecture Notes Statist. Proc. 198),Springer,Heidelberg, pp. 257–265.CrossRefGoogle Scholar
[9] Cherubini, U.,Luciano, E. and Vecchiato, W. (2004).Copula Methods in Finance.John Wiley,Chichester.CrossRefGoogle Scholar
[10] Chevallier, J. (2011).Detecting instability in the volatility of carbon prices.Energy Economics 33,99–110.CrossRefGoogle Scholar
[11] Chevallier, J. (2012).Econometric Analysis of Carbon Markets: The European Union Emissions Trading Scheme and the Clean Development Mechanism.Springer,Dordrecht.CrossRefGoogle Scholar
[12] Demko , S.,Moss, W. F. and Smith, P. W. (1984).Decay rates for inverses of band matrices.Math. Comput. 43,491–499.CrossRefGoogle Scholar
[13] Dias, A. and Embrechts, P. (2009).Testing for structural changes in exchange rates' dependence beyond linear correlation.Europ. J. Finance 15,619–637.CrossRefGoogle Scholar
[14] Dias, A. and Embrechts, P. (2010).Modeling exchange rate dependence dynamics at different time horizons.J. Internat. Money Finance 29,1687–1705.CrossRefGoogle Scholar
[15] Dobrić, J. and Schmid, F. (2007).A goodness of fit test for copulas based on Rosenblatt's transformation.Comput. Statist. Data Anal. 51,4633–4642.CrossRefGoogle Scholar
[16] Embrechts, P. (2009).Copulas: A personal view. J. Risk Insurance 76,639–650.CrossRefGoogle Scholar
[17] Fernández, B. and Muriel, N. (2009).Regular variation and related results for the multivariate GARCH(p,q) model with constant conditional correlations.J. Multivariate Anal. 100,1538–1550.CrossRefGoogle Scholar
[18] Fisher, R. A. (1970).Statistical Methods for Research Workers,14th edn.Oliver and Boyd,Edinburgh.Google Scholar
[19] Gaisser, S.,Memmel, C.,Schmidt, R. and Wehn, C. (2009).Time dynamic and hierarchical dependence modelling of an aggregated portfolio of trading books: a multivariate nonparametric approach. Discussion Paper Series 2: Banking and Financial Studies 2009,07.Deutsche Bundesbank,Frankfurt am Main.Google Scholar
[21] Genest, C.,Ghoudi, K. and Rivest, L.-P. (1995).A semiparametric estimation procedure of dependence parameters in multivariate families of distributions.Biometrika 82,543–552.CrossRefGoogle Scholar
[21] Genest, C.,Rémillard, B. and Beaudoin, D. (2009).Goodness-of-fit tests for copulas: A review and a power study.Insurance Math. Econom. 44,199–213.CrossRefGoogle Scholar
[22] Giacomini, E.,Härdle, W. and Spokoiny, V. (2009).Inhomogeneous dependence modelling with time-varying copulae.J. Business Econom. Statist. 27,224–234.CrossRefGoogle Scholar
[23] Hafner, C. M. and Manner, H. (2012).Dynamic stochastic copula models: estimation, inference and applications.J. Appl. Econometrics 27,269–295.CrossRefGoogle Scholar
[24] Hansen, P. R. and Lunde, A. (2005).A comparison of volatility models: does anything beat a GARCH(1,1)?J. Appl. Econometrics 20,873–889.CrossRefGoogle Scholar
[25] Härdle, W. K.,Okhrin, O. and Okhrin, Y. (2008).Modeling dependencies with copulae. In Applied Quantitative Finance,2nd edn., eds W. K. Härdle, N. Hautsch and L. Overbeck,Springer,Berlin, pp. 3–36.Google Scholar
[26] Lehmann, E. L. and Romano, J. P. (2005).Testing Statistical Hypotheses,3rd edn.Springer,New York.Google Scholar
[27] Mai, J.-F. and Scherer, M. (2012).Simulating Copulas: Stochastic Models, Sampling Algorithms, and Applications (Ser. Quant. Finance 4).Imperial College Press,London.CrossRefGoogle Scholar
[28] Mai, J.-F. and Scherer, M. (2014).Financial Engineering with Copulas Explained.Palgrave Macmillan,Basingstoke.CrossRefGoogle Scholar
[29] Mikosch, T. and Starica, C. (2000).Limit theory for the sample autocorrelations and extremes of a GARCH(1,1) process.Ann. Statist. 28,1427–1451.CrossRefGoogle Scholar
[30] Mroz, M. (2012).Time-varying copula models for financial time series. Doctoral Thesis, Ulm University.Google Scholar
[31] Nelson, D. B. (1991).Conditional heteroskedasticity in asset returns: a new approach.Econometrica 59,347–370.CrossRefGoogle Scholar
[32] Patton, A. J. (2012).A review of copula models for economic time series.J. Multivariate Anal. 110,4–18.CrossRefGoogle Scholar
[33] Simes, R. J. (1986).An improved Bonferroni procedure for multiple tests of significance.Biometrika 73,751–754.CrossRefGoogle Scholar
[34] Stöber, J. and Czado, C. (2012).Detecting regime switches in the dependence structure of high dimensional financial data. Preprint. Available at http://arxiv.org/abs/1202.2009v1.Google Scholar
[35] Teriokhin, A. T.,de Meeǻs, T. and Guégan, J.-F. (2007).On the power of some binomial modifications of the Bonferroni multiple test.J. General Biology 68,332–340.Google ScholarPubMed
[36] Yaskov, P. (2010).Testing for predictive ability in the presence of structural breaks.Quantile 8,127–135 (in Russian).Google Scholar