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A test for Archimedeanity in bivariate copula models

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  • Bücher, Axel
  • Dette, Holger
  • Volgushev, Stanislav

Abstract

We propose a new test for the hypothesis that a bivariate copula is an Archimedean copula which can be used as a preliminary step before further dependence modeling. The corresponding test statistic is based on a combination of two measures resulting from the characterization of Archimedean copulas by the property of associativity and by a strict upper bound on the diagonal by the Fréchet–Hoeffding upper bound. We prove weak convergence of this statistic and show that the critical values of the corresponding test can be determined by the multiplier bootstrap method. The test is shown to be consistent against all departures from Archimedeanity. A simulation study is presented which illustrates the finite-sample properties of the new test.

Suggested Citation

  • Bücher, Axel & Dette, Holger & Volgushev, Stanislav, 2012. "A test for Archimedeanity in bivariate copula models," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 121-132.
    • Handle: RePEc:eee:jmvana:v:110:y:2012:i:c:p:121-132
    DOI: 10.1016/j.jmva.2012.01.026
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    2. Mensi, Walid & Shahzad, Syed Jawad Hussain & Hammoudeh, Shawkat & Zeitun, Rami & Rehman, Mobeen Ur, 2017. "Diversification potential of Asian frontier, BRIC emerging and major developed stock markets: A wavelet-based value at risk approach," Emerging Markets Review, Elsevier, vol. 32(C), pages 130-147.
    3. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    4. Montes, Ignacio & Montes, Susana, 2016. "Stochastic dominance and statistical preference for random variables coupled by an Archimedean copula or by the Fr e ´ chet–Hoeffding upper bound," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 275-298.
    5. Samitas, Aristeidis & Tsakalos, Ioannis, 2013. "How can a small country affect the European economy? The Greek contagion phenomenon," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 25(C), pages 18-32.
    6. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    7. Bücher Axel & Jaser Miriam & Min Aleksey, 2021. "Detecting departures from meta-ellipticity for multivariate stationary time series," Dependence Modeling, De Gruyter, vol. 9(1), pages 121-140, January.
    8. Shegorika Rajwani & Dilip Kumar, 2019. "Measuring Dependence Between the USA and the Asian Economies: A Time-varying Copula Approach," Global Business Review, International Management Institute, vol. 20(4), pages 962-980, August.

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