This paper considers estimating semiparametric copula-based multivariate dynamic models(Chen and Fan (2006)) in multiple stages. In the first stage, univariate semiparametric GARCH models are used to prefilter temporal dependence of individual financial series. In the second stage, filtered residuals are used to estimate nonparametric marginal distributions and copula dependence parameters. We propose joint estimation of marginal distributions and copula parameters via pseudo sieve maximum likelihood because it seems to give more precise estimates in real applications. Furthermore, we derive the first-order asymptotic effect of the semiparametric GARCH first stage on pseudo sieve MLE and two-step procedure.
JEL classification: C14; C22; G32.
Key Words: Multivariate dynamic models; Semiparametric inference; Copula; Pseudo sieve maximum likelihood.