Semiparametric Estimation and Variable Selection for Single-index Copula Models

A copula model with flexibly specified dependence structure can be useful to capture the complexity and heterogeneity in economic and financial time series. However, there exists little methodological guidance for the specification process using copulas. This paper contributes to fill this gap by considering the recently proposed single-index copulas, for which we propose a simultaneous estimation and variable selection procedure. The proposed method allows to choose the most relevant state variables from a comprehensive set using a penalized estimation, and we derive its large sample properties. Simulation results demonstrate the good performance of the proposed method in selecting the appropriate state variables and estimating the unknown index coefficients and dependence parameters. An application of the new procedure identifies six macroeconomic driving factors for the dependence among U.S. housing markets.