Semiparametric Conditional Mixture Copula Models with Copula Selection

This study proposes a semiparametric conditional mixture copula model, that allows for unspecified functions of a covariate in both the (conditional) marginal distributions and the copula dependence and weight parameters. To estimate this model, we propose a two-step procedure. In the first step, the (conditional) marginal distributions are nonparametrically estimated using the weighted Nadaraya- Watson method. In the second step, we apply a penalized local log-likelihood function with a penalty term to simultaneously estimate the copula parameters and choose an appropriate copula model. Furthermore, we propose a test of covariate effects for time series data. We establish the large sample properties of both the penalized and unpenalized estimators based on alpha-mixing conditions. Monte Carlo simulations show that the proposed method performs well in selecting and estimating conditional mixture copulas under various model specifications. Finally, we apply the proposed method to investigate the dynamic patterns of dependence among four states' housing markets along the interest rate path.