This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric invariant (or marginal) distributions and parametric copula functions that capture the temporal dependence of the processes; the implied transition distributions are all semiparametric. Models in this class are easy to simulate, and can be expressed as semiparametric regression transformation models. One advantage of this copula approach is to separate out the temporal dependence (such as tail dependence) from the marginal behavior (such as fat tailedness) of a time series. We present conditions under which processes generated by models in this class are β-mixing; naturally, these conditions depend only on the copula specification. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. Estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles are easily obtained from estimators of the marginal distribution and the copula parameter; their √ n− consistency and asymptotic normality can be obtained using the Delta method. In addition, the semiparametric conditional quantile estimators are automatically monotonic across quantiles.JEL Classification: C14; C22
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We introduce a new class of semiparametric copula-based multivariate dynamic (SCOMDY) models, which specify the conditional mean and the conditional variance of a multivariate time series parametrically, but specify the multivariate distribution of the standardized innovation semiparametrically as a parametric copula evaluated at nonparametric marginal distributions. We first study large sample properties of the estimators of SCOMDY model parameters under a misspecified parametric copula, then propose pseudo likelihood ratio (PLR) tests for model selection between two SCOMDY models with possibly misspecified copulas, and finally develop PLR tests for model selection between more than two SCOMDY models. The limiting null distributions of the PLR tests do not depend on the estimation of conditional mean and conditional variance parameters, hence are very easy to simulate. Empirical applications to three and higher dimensional daily exchange rate series indicate that a SCOMDY model with a tail-dependent copula is generally preferred. r
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