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Estimation of Copula-Based Semiparametric Time Series Models

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Author Info
Yanqin Fan
Xiaohong Chen
Abstract

This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric invariant (or marginal) distributions and parametric copula functions that capture the temporal dependence of the processes; the implied transition distributions are all semiparametric. Models in this class are easy to simulate, and can be expressed as semiparametric regression transformation models. One advantage of this copula approach is to separate out the temporal dependence(such as tail dependence) from the marginal behavior (such as fat tailedness) of a time series. We present conditions under which processes generated by models in this class are $\beta $-mixing; naturally, these conditions depend only on the copula specification. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. Estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles are easily obtained from estimators of the marginal distribution and the copula parameter; their $\sqrt{n}-$ consistency and asymptotic normality can be obtained using the Delta method. In addition, the semiparametric conditional quantile estimators are automatically monotonic across quantiles.

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Paper provided by Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 559.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:feam04:559

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Related research
Keywords: Copula; Nonlinear Markov models; Semiparametric estimation; Conditional quantile;

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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  1. Granger, Clive W.J. & Teräsvirta, Timo & Patton, Andrew J., 2002. "Common factors in conditional distributions," Working Paper Series in Economics and Finance 515, Stockholm School of Economics.
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  2. Xiaohong Chen & Yanqin Fan, 2002. "Evaluating Density Forecasts via the Copula Approach," Working Papers 0225, Department of Economics, Vanderbilt University, revised Sep 2003. [Downloadable!]
  3. Andrew Patton, 2001. "Estimation of Copula Models for Time Series of Possibly Different Length," University of California at San Diego, Economics Working Paper Series 2001-17, Department of Economics, UC San Diego. [Downloadable!]
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  7. Andrew J. Patton, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series 2001-09, Department of Economics, UC San Diego. [Downloadable!]
  8. Joshua Rosenberg, 1999. "Semiparametric Pricing of Multivariate Contingent Claims," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-028, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  12. Patrick Gagliardini ; Christian Gourieroux, 2002. "Duration Time Series Models with Proportional Hazard," Working Papers 2002-21, Centre de Recherche en Economie et Statistique. [Downloadable!]
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  17. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168. [Downloadable!] (restricted)
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