Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification
Working Paper No. 04-W19
Xiaohong Chen and Yanqin Fan
ABSTRACT [article]
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.
Keywords and Phrases: Multivariate dynamic models, misspecified copulas, multiple
model selection, semiparametric inference, mixture copulas, t copula, Gaussian copula
JEL Classification Number: C14, C22, G22