In this paper we propose the adaptive lasso for predictive quantile regression (ALQR). Reflecting empirical findings, we allow predictors to have various degrees of persistence and exhibit different signal strengths. The number of predictors is allowed to grow with the sample size. We study regularity conditions under which stationary, local unit root, and cointegrated predictors are present simultaneously. We next show the convergence rates and model selection consistency of ALQR. We apply the proposed method to the out-of-sample quantile prediction problem of stock returns and find that it outperforms the existing alternatives. We also provide numerical evidence from additional Monte Carlo experiments, supporting the theoretical results.

翻译：在本文中,我们提出用于预测四分位回归的适应性拉索(ALQR) 。 反映实证结果, 我们允许预测者具有不同程度的持久性, 并表现出不同的信号强度。 允许预测者的数量随着样本大小而增长。 我们研究固定、 本地单位根和共集预测器同时存在的常规性条件。 我们接下来展示ALQR的趋同率和模型选择一致性。 我们用建议的方法来应对储量回报的超抽样预测问题, 并发现它优于现有的替代物。 我们还从其他蒙特卡洛实验中提供数字证据, 支持理论结果 。