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Estimation of Copula-Based Semiparametric Time Series Models

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Author Info
Xiaohong Chen () (Department of Economics, New York University)
Yanqin Fan () (Department of Economics, Vanderbilt University)
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, and a member in this class can be expressed as a generalized semiparametric regression transformation model. One advantage of this copula approach is to separate out the temporal dependence (such as clustering, tail dependence) from the marginal behavior (such as asymmetry, fat tails) 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. These results allow us to easily obtain the root-n consistent and asymptotically normal estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles. In addition, the semiparametric conditional quantile estimators are automatically monotonic across quantiles, which is attractive for portfolio conditional value-at-risk calculation.

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File URL: http://www.vanderbilt.edu/Econ/wparchive/workpaper/vu02-w26R.pdf
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File Function: Revised version, 2004
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Paper provided by Department of Economics, Vanderbilt University in its series Working Papers with number 0226.

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Date of creation: Oct 2002
Date of revision: Oct 2004
Handle: RePEc:van:wpaper:0226

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Related research
Keywords: Copula; beta-mixing; semiparametric estimation; parametric bootstrap;

Other versions of this item:

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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    Other versions:
  2. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-12, March. [Downloadable!] (restricted)
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    Other versions:
  4. Xiaohong Chen & Yanqin Fan, 2002. "Evaluating Density Forecasts via the Copula Approach," Working Papers 0225, Department of Economics, Vanderbilt University, revised Sep 2003. [Downloadable!]
  5. 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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  16. 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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  19. Xiaohong Chen & Lars P. Hansen & Marine Carrasco, 2008. "Nonlinearity and Temporal Dependence," Cowles Foundation Discussion Papers 1652, Cowles Foundation, Yale University. [Downloadable!]
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  20. Yanqin Fan & Xiaohong Chen & Andrew Patton, 2004. "(IAM Series No 003) Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates," FMG Discussion Papers dp483, Financial Markets Group. [Downloadable!] (restricted)
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