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Multivariate Markov Families of Copulas

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For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.
Opis fizyczny
  • Justus-Liebig Universität Gießen, Institut of Mathematics, 35392 Gießen
  • Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt am Main
  • [1] Abegaz, F. and Naik-Nimbalkar, U. (2008). Modeling statistical dependence of Markov chains via copula models. J. Statist. Plann. Inference, 138(4), 1131–1146.
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  • [7] Chen, X. and Fan, Y. (2006) Estimation of copula-based semiparametric time series models. J. Econometrics, 130, 307–335.
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  • [14] Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall/CRC.
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  • [17] Rémillard, B., Papageorgiou, N., and Soustra, F. (2012) Copula-based semiparametric models for multivariate time series. J. Multivariate Anal., 110, 30–42. [WoS]
  • [18] Simard, C. and Rémillard, B. (2015) Forecasting time series with multivariate copulas. Depend. Model., 3, 59–82.
  • [19] Stöber, J. and Czado, C. (2014) Regime switches in the dependence structure of multidimensional financial data. Comput. Stat. Data An., 76, 672–686. [WoS]
  • [20] Yi,W. and Liao, S.S. (2010) Statistical properties of parametric estimators forMarkov chain vectors based on copula models. J. Statist. Plann. Inference, 140, 1465–1480.
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