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Weighted power mean copulas: Theory and application

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  • Klein, Ingo
  • Fischer, Matthias J.
  • Pleier, Thomas

Abstract

It is well known that the arithmetic mean of two possibly different copulas forms a copula, again. More general, we focus on the weighted power mean (WPM) of two arbitrary copulas which is not necessary a copula again, as different counterexamples reveal. However, various conditions regarding the mean function and the underlying copula are given which guarantee that a proper copula (so-called WPM copula) results. In this case, we also derive dependence properties of WPM copulas and give some brief application to financial return series.

Suggested Citation

  • Klein, Ingo & Fischer, Matthias J. & Pleier, Thomas, 2011. "Weighted power mean copulas: Theory and application," FAU Discussion Papers in Economics 01/2011, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2011.
    • Handle: RePEc:zbw:iwqwdp:012011
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    References listed on IDEAS

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    1. Feicht, Robert & Stummer, Wolfgang, 2010. "Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery," FAU Discussion Papers in Economics 05/2010, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    2. Matthias Fischer & Christian Kock & Stephan Schluter & Florian Weigert, 2009. "An empirical analysis of multivariate copula models," Quantitative Finance, Taylor & Francis Journals, vol. 9(7), pages 839-854.
    3. Mosthaf, Alexander & Schnabel, Claus & Stephani, Jens, 2011. "Low-wage careers: Are there dead-end firms and dead-end jobs?," Zeitschrift für ArbeitsmarktForschung - Journal for Labour Market Research, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 43(3), pages 231-249.
    4. Fischer, Matthias J. & Gao, Yang & Herrmann, Klaus, 2010. "Volatility models with innovations from new maximum entropy densities at work," FAU Discussion Papers in Economics 03/2010, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    5. Fischer, Matthias J. & Klein, Ingo, 2007. "Some results on weak and strong tail dependence coefficients for means of copulas," Discussion Papers 78/2007, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    6. Robert Feicht & Wolfgang Stummer, 2010. "Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary," DEGIT Conference Papers c015_041, DEGIT, Dynamics, Economic Growth, and International Trade.
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    Cited by:

    1. Klein, Ingo & Christa, Florian, 2011. "Families of copulas closed under the construction of generalized linear means," FAU Discussion Papers in Economics 04/2011, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    2. Schnitzlein, Daniel D., 2012. "How important is cultural background for the level of intergenerational mobility?," Economics Letters, Elsevier, vol. 114(3), pages 335-337.
    3. Hakim Bekrizadeh & Babak Jamshidi, 2017. "A new class of bivariate copulas: dependence measures and properties," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 31-50, April.

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    Keywords

    Copulas; generalized power mean; max id; left tail decreasing; tail dependence;
    All these keywords.

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