Variable selection via quantile regression with the process of Ornstein-Uhlenbeck type

Based on the data-cutoff method,we study quantile regression in linear models,where the noise process is of Ornstein-Uhlenbeck type with possible jumps.In single-level quantile regression,we allow the noise process to be heteroscedastic,while in composite quantile regression,we require that the noise process be homoscedastic so that the slopes are invariant across quantiles.Similar to the independent noise case,the proposed quantile estimators are root-n consistent and asymptotic normal.Furthermore,the adaptive least absolute shrinkage and selection operator(LASSO)is applied for the purpose of variable selection.As a result,the quantile estimators are consistent in variable selection,and the nonzero coefficient estimators enjoy the same asymptotic distribution as their counterparts under the true model.Extensive numerical simulations are conducted to evaluate the performance of the proposed approaches and foreign exchange rate data are analyzed for the illustration purpose.