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

Author

Listed:
  • Xiaohong Chen

    (Department of Economics, New York University)

  • Yanqin Fan

    (Department of Economics, Vanderbilt University)

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.

Suggested Citation

  • Xiaohong Chen & Yanqin Fan, 2004. "Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification," Vanderbilt University Department of Economics Working Papers 0419, Vanderbilt University Department of Economics, revised Sep 2004.
  • Handle: RePEc:van:wpaper:0419
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Multivariate dynamic models; Misspecified copulas; Multiple model selection; Semiparametric inference; Mixture copulas; t copula; Gaussian copula;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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