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Archimedean Copulas And Temporal Dependence

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  • Beare, Brendan K.

Abstract

We study the dependence properties of stationary Markov chains generated by Archimedean copulas. Under some simple regularity conditions, we show that regular variation of the Archimedean generator at zero and one implies geometric ergodicity of the associated Markov chain. We verify our assumptions for a range of Archimedean copulas used in applications.

Suggested Citation

  • Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(06), pages 1165-1185, December.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:06:p:1165-1185_00
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    6. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
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    Cited by:

    1. Overbeck Ludger & Schmidt Wolfgang M., 2015. "Multivariate Markov Families of Copulas," Dependence Modeling, De Gruyter Open, vol. 3(1), pages 1-13, October.
    2. Beatriz Vaz de Melo Mendes & Cecília Aíube, 2011. "Copula based models for serial dependence," International Journal of Managerial Finance, Emerald Group Publishing, vol. 7(1), pages 68-82, February.
    3. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(05), pages 923-960, October.
    4. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Estimating non-linear serial and cross-interdependence between financial assets," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 837-846.
    5. Oleg Sokolinskiy & Dick van Dijk, 2011. "Forecasting Volatility with Copula-Based Time Series Models," Tinbergen Institute Discussion Papers 11-125/4, Tinbergen Institute.
    6. Demian Pouzo, 2015. "On the Non-Asymptotic Properties of Regularized M-estimators," Papers 1512.06290, arXiv.org, revised Oct 2016.
    7. Simard Clarence & Rémillard Bruno, 2015. "Forecasting time series with multivariate copulas," Dependence Modeling, De Gruyter Open, vol. 3(1), pages 1-24, May.
    8. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    9. Elena Di Bernardino & Didier Rullière, 2016. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Post-Print hal-00992707, HAL.
    10. Fermanian, Jean-David & Wegkamp, Marten H., 2012. "Time-dependent copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 19-29.
    11. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    12. Cherubini, Umberto & Mulinacci, Sabrina & Romagnoli, Silvia, 2011. "A copula-based model of speculative price dynamics in discrete time," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1047-1063, July.
    13. Rub'en Loaiza-Maya & Michael S. Smith & Worapree Maneesoonthorn, 2017. "Time Series Copulas for Heteroskedastic Data," Papers 1701.07152, arXiv.org.
    14. Longla, Martial & Peligrad, Magda, 2012. "Some aspects of modeling dependence in copula-based Markov chains," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 234-240.
    15. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Economics Series Working Papers 655, University of Oxford, Department of Economics.
    16. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    17. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
    18. Sebastian Kiwitt & Natalie Neumeyer, 2013. "A note on testing independence by a copula-based order selection approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 62-82, March.
    19. Longla, Martial, 2015. "On mixtures of copulas and mixing coefficients," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 259-265.
    20. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    21. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, Elsevier.

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