Variable selection via composite quantile regression with dependent errors

We propose composite quantile regression for dependent data, in which the errors are from short-range dependent and strictly stationary linear processes. Under some regularity conditions, we show that composite quantile estimator enjoys root-n consistency and asymptotic normality. We investigate the asymptotic relative efficiency of composite quantile estimator to both single-level quantile regression and least-squares regression. When the errors have finite variance, the relative efficiency of composite quantile estimator with respect to the least-squares estimator has a universal lower bound. Under some regularity conditions, the adaptive least absolute shrinkage and selection operator penalty leads to consistent variable selection, and the asymptotic distribution of the non-zero coefficient is the same as that of the counterparts obtained when the true model is known. We conduct a simulation study and a real data analysis to evaluate the performance of the proposed approach.