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Tytuł artykułu

Multivariate Markov Families of Copulas

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-07-08
zaakceptowano
2015-10-09
online
2015-10-26
Twórcy
  • Justus-Liebig Universität Gießen, Institut of Mathematics, 35392 Gießen
  • Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt am Main
Bibliografia
  • [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.
  • [2] Beare, B.K. (2010). Copulas and temporal dependence. Econometrica, 78(1), 395–410.[WoS][Crossref]
  • [3] Beare, B.K. and Seo, J. (2015) Vine copula specification for stationary multivariate Markov chains. J. Time Series Anal., 36,228–246.
  • [4] Bielecki, T. R., Crépey, S., Jeanblanc, M., and Zargari, B. (2012). Valuation and hedging of CDS counterparty exposure in aMarkov copula model. Int. J. Theor. Appl. Finance, 15(01).[Crossref]
  • [5] Bielecki, T. R., Jakubowski, J., Vidozzi, A., and Vidozzi, L. (2008). Study of dependence for some stochastic processes. Stoch.Anal. Appl., 26(4), 903–924.[Crossref]
  • [6] Brechmann, E.C., Czado, C., and Aas, K. (2012) Truncated regular vines in high dimensions with application to financial data.Canad. J. Statist., 40 (1), 68-85.
  • [7] Chen, X. and Fan, Y. (2006) Estimation of copula-based semiparametric time series models. J. Econometrics, 130, 307–335.
  • [8] Chen, X. , Wu, W.B., and Yi, Y. (2009) Efficient estimation of copula-based semiparametric Markov models. Ann. Statist., 37(6B), 4214-4253.[Crossref]
  • [9] Cherubini, U., Mulinacci, S., Gobbi, F., and Romagnoli, S. (2011a). Dynamic Copula Methods in Finance. Wiley.
  • [10] Cherubini, U., Mulinacci, S., and Romagnoli, S. (2011b). A copula-based model of speculative price dynamics in discretetime. J. Multivariate Anal., 102(6), 1047–1063.[WoS][Crossref]
  • [11] Darsow, W., Nguyen, B., and Olsen, E. (1992). Copulas and Markov processes. Illinois J. Math, 36(4), 600–642.
  • [12] Haff, I.H. (2012) Estimating the parameters of a pair copula construction. Bernoulli, 19(2), 462–491.[Crossref]
  • [13] Ibragimov, R. (2009). Copula-based characterizations for higher order Markov processes. Econometric Theory, 25(03),819–846.[WoS][Crossref]
  • [14] Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall/CRC.
  • [15] McNeil, A.J., Frey, R., and Embrechts, P. (2010). Quantitative Risk Management: Concepts, Techniques, and Tools. PrincetonUniversity Press.
  • [16] Nelsen, R. (1999). An Introduction to Copulas. Springer Verlag, New York.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_demo-2015-0011
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