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Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification

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  • Xiaohong Chen

    ()
    (Department of Economics, New York University)

  • Yanqin Fan

    ()
    (Department of Economics, Vanderbilt University)

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    Abstract

    Recently Chen and Fan (2003a) introduced a new class of semiparametric copula-based multivariate dynamic (SCOMDY) models. A SCOMDY model specifies the conditional mean and the conditional variance of a multivariate time series parametrically (such as VAR, GARCH), but specifies the multivariate distribution of the standardized innovation semiparametrically as aparametric copula evaluated at nonparametric marginal distributions. In this paper, we first study large sample properties of the estimators of SCOMDY model parameters under a misspecified parametric copula, and then establish pseudo likelihood ratio (PLR) tests for model selection between two SCOMDY models with possibly misspecified copulas. Finally we develop PLR tests for model selection between more than two SCOMDY models along the lines of the reality check of White (2000). The limiting distributions of the estimators of copula parameters and the PLR tests do not depend on the estimation of conditional mean and conditional variance parameters. Although the tests are affected by the estimation of unknown marginal distributions of standardized innovations, they have standard parametric rates and the limiting null distributions are very easy to simulate. Empirical applications to multiple daily exchange rate data indicate the simplicity and usefulness of the proposed tests. Although a SCOMDY model with Gaussian copula might be a reasonable model for some bivariate FX series, but a SCOMDY model with a copula which has (asymmetric) tail-dependence is generally preferred for tri-variate and higher dimensional FX series.

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    File URL: http://www.accessecon.com/pubs/VUECON/vu04-w19.pdf
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    Bibliographic Info

    Paper provided by Vanderbilt University Department of Economics in its series Vanderbilt University Department of Economics Working Papers with number 0419.

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    Date of creation: Feb 2004
    Date of revision: Sep 2004
    Handle: RePEc:van:wpaper:0419

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    Web page: http://www.vanderbilt.edu/econ/wparchive/index.html

    Related research

    Keywords: Multivariate dynamic models; Misspecified copulas; Multiple model selection; Semiparametric inference; Mixture copulas; t copula; Gaussian copula;

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    1. 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.
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