High‐dimensional macroeconomic forecasting and variable selection via penalized regression

This study examines high-dimensional forecasting and variable selection via folded-concave penalized regressions. The penalized regression approach leads to sparse estimates of the regression coefficients and allows the dimensionality of the model to be much larger than the sample size. First, we discuss the theoretical aspects of a penalized regression in a time series setting. Specifically, we show the oracle inequality with ultra-high-dimensional time-dependent regressors. Then we show the validity of the penalized regression using two empirical applications. First, we forecast quarterly US gross domestic product data using a high-dimensional monthly data set and the mixed data sampling (MIDAS) framework with penalization. Second, we examine how well the penalized regression screens a hidden portfolio based on a large New York Stock Exchange stock price data set. Both applications show that a penalized regression provides remarkable results in terms of forecasting performance and variable selection.

本研究通过折叠凹惩罚回归检验高维预测和变量选择。惩罚回归方法导致回归系数的稀疏估计，并允许模型的维度远大于样本量。首先，我们讨论时间序列环境下惩罚回归的理论方面。具体而言，我们展示了具有超高维时间相关回归变量的神谕不等式。然后，我们通过两个实证应用展示惩罚回归的有效性。首先，我们使用高维月度数据集和带惩罚的混合数据抽样（MIDAS）框架预测美国季度国内生产总值数据。其次，我们基于一个大型纽约证券交易所股票价格数据集检验惩罚回归对隐藏投资组合的筛选效果。这两个应用都表明，惩罚回归在预测性能和变量选择方面提供了显著的结果。