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Copulas and Temporal Dependence

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  • Brendan K. Beare

Abstract

An emerging literature in time series econometrics concerns the modeling of potentially nonlinear temporal dependence in stationary Markov chains using copula functions. We obtain sufficient conditions for a geometric rate of mixing in models of this kind. Geometric β-mixing is established under a rather strong sufficient condition that rules out asymmetry and tail dependence in the copula function. Geometric ρ-mixing is obtained under a weaker condition that permits both asymmetry and tail dependence. We verify one or both of these conditions for a range of parametric copula functions that are popular in applied work. Copyright 2010 The Econometric Society.

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  • Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
  • Handle: RePEc:ecm:emetrp:v:78:y:2010:i:1:p:395-410
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    1. McCausland, William J., 2007. "Time reversibility of stationary regular finite-state Markov chains," Journal of Econometrics, Elsevier, vol. 136(1), pages 303-318, January.
    2. P. Gagliardini & C. Gourieroux, 2008. "Duration time-series models with proportional hazard," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 74-124, January.
    3. Chen, Xiaohong & Hansen, Lars Peter & Carrasco, Marine, 2010. "Nonlinearity and temporal dependence," Journal of Econometrics, Elsevier, vol. 155(2), pages 155-169, April.
    4. Lorraine Dearden & Emla Fitzsimons & Alissa Goodman & Greg Kaplan, 2008. "Higher Education Funding Reforms in England: The Distributional Effects and the Shifting Balance of Costs," Economic Journal, Royal Economic Society, vol. 118(526), pages 100-125, February.
    5. Gagliardini, Patrick & Gourieroux, Christian, 2007. "An efficient nonparametric estimator for models with nonlinear dependence," Journal of Econometrics, Elsevier, vol. 137(1), pages 189-229, March.
    6. Rustam Ibragimov, 2005. "Copula-Based Dependence Characterizations and Modeling for Time Series," Harvard Institute of Economic Research Working Papers 2094, Harvard - Institute of Economic Research.
    7. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    8. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
    9. Brendan K. Beare, 2007. "A New Mixing Condition," Economics Series Working Papers 348, University of Oxford, Department of Economics.
    10. Arcones, Miguel A., 1995. "On the central limit theorem for U-statistics under absolute regularity," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 245-249, August.
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