Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification
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.
This item appears in the following collection(s):
Showing items related by title, author, creator and subject.
Callaway, Brantly Mercer IV (2016-04-09)Department: EconomicsIn my dissertation, I develop new methods to understand the distributional effect of participating in a program or experiencing a treatment. This goal is different from most research in economics which either (i) restricts ...
Chen, Xiaohong; Fan, Yanqin; Tsyrennikov, Victor (Vanderbilt University, 2004)We propose a sieve maximum likelihood (ML) estimation procedure for a broad class of semiparametric multivariate distribution models. A joint distribution in this class is characterized by a parametric copula function ...
Chen, Xiaohong; Fan, Yanqin (Vanderbilt University, 2004)In this paper, we address two important issues in survival model selection for censored data generated by the Archimedean copula family; method of estimating the parametric copulas and data reuse. We demonstrate that for ...