Multivariate Markov Families of Copulas

• Autorzy: Ludger Overbeck , Wolfgang M. Schmidt
• 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.

Słowa kluczowe

EN

Markov process; copula; Chapman–Kolmogorov equation

Kategorie tematyczne

• 60J05: Discrete-time Markov processes on general state spaces
• 60G07: General theory of processes
• 60J25: Continuous-time Markov processes on general state spaces

• Wydawca: De Gruyter Open
• Czasopismo: Dependence Modeling
• Rocznik: 2015
• Tom: 3
• Numer: 1

Daty

otrzymano

2015-07-08

zaakceptowano

2015-10-09

online

2015-10-26

Twórcy

autor

Ludger Overbeck

• Justus-Liebig Universität Gießen, Institut of Mathematics, 35392 Gießen

autor

Wolfgang M. Schmidt

• Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt am Main

Bibliografia

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• [4] Bielecki, T. R., Crépey, S., Jeanblanc, M., and Zargari, B. (2012). Valuation and hedging of CDS counterparty exposure in a Markov copula model. Int. J. Theor. Appl. Finance, 15(01). [Crossref]
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• [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 discrete time. 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. Princeton University 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.

Identyfikatory

DOI

10.1515/demo-2015-0011