SummaryThis 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.

中文翻译：

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高维宏观经济预测和基于惩罚回归的变量选择

总结本研究通过折叠-凹惩罚回归分析了高维预测和变量选择。惩罚性回归方法导致回归系数的稀疏估计，并使模型的维数比样本大小大得多。首先，我们讨论时间序列设置中惩罚回归的理论方面。具体来说，我们显示了超高维时间相关回归变量的oracle不等式。然后，我们使用两个经验应用来证明惩罚回归的有效性。首先，我们使用高维月度数据集和带有惩罚性的混合数据采样（MIDAS）框架来预测美国季度国内生产总值数据。第二，我们研究了基于大型纽约股票交易所股票价格数据集的惩罚式回归筛选隐藏的投资组合的效果如何。两种应用都表明，惩罚回归在预测性能和变量选择方面提供了显着的结果。