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Unformatted text preview: Copula-based Dependence Models of Two Markov Time Series of Order 1 YI Wen-de School of Economics & Management, Southwest Jiaotong University, Chengdu, Sichuan 610031;Dept. of Math & Computer Science, Chongqing University of Arts and Sciences Yongchuan Chongqing,China,402160 Abstract We study the dependence model of 2-dimensional stationary Markov chains based on the copula functions using the theory of conditional probability distributions. In this paper the temporal dependence and the contemporaneous dependence models are proposed by giving the time series values at time 1 t- . In addition we propose a three-stage parametric pseudo likelihood estimation procedure for the marginal parameters and the dependence parameters. Keywords Temporal dependence; Contemporaneous dependence; Markov chain; Copula; Three-stage estimation 1. Introduction The application of copulas in various fields appears to be a recent phenomenon; especially modeling temporal of time series data using copulas has recently gained much attention (see among others Joe, 1997  ;Chen and Fan, 2006  ). By Sklar’s (1959) theorem  , one can always model any multivariate distribution and its copula function separately, where the copula captures all the scale-free dependence in the multivariate distribution. Because of this flexibility, copula have gained popularity in the finance and insurance community in the past few years, where modeling and estimating the dependence structure between several univariate time series are of great interest; for reviews see Frees and Valdez(1998)  and Embrechts et al. (2002)  . While considering the dependence of the time series vector we must calculate the contemporaneous dependence between several univariate time series and the temporal dependence of the time series vector at the same time. In the copula approach to univariate time series modeling, the finite dimension distributions of the time series are generated by copulas. By coupling different marginal distributions with different copula functions, copula-based time series models are able to model a wide variety of marginal behaviors (such as skewness and fat tails) and dependence properties (such as clusters, positive or negative tail dependence). Darsow et al. (1992)  provide a necessary and sufficient condition for a copula-based time series to be a Markov models based process. Joe (1997)  proposes a class of parametric stationary Markov models based on parametric copula and parametric marginal distributions, and provides an application to daily air quality measurements. YI We-de and WEI Gui-wu  investigate the reliability of dependence-parts vote system based on copula functions....
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