This study introduces a bootstrap test of the validity of factor regression within a high-dimensional factor-augmented sparse regression model that integrates factor and sparse regression techniques. The test provides a means to assess the suitability of the classical dense factor regression model compared to a sparse plus dense alternative augmenting factor regression with idiosyncratic shocks. Our proposed test does not require tuning parameters, eliminates the need to estimate covariance matrices, and offers simplicity in implementation. The validity of the test is theoretically established under time-series dependence. Through simulation experiments, we demonstrate the favorable finite sample performance of our procedure. Moreover, using the FRED-MD dataset, we apply the test and reject the adequacy of the classical factor regression model when the dependent variable is inflation but not when it is industrial production. These findings offer insights into selecting appropriate models for high-dimensional datasets.

翻译：本研究针对高维因子增强稀疏回归模型，提出了一种检验因子回归有效性的自助法。该模型融合了因子回归与稀疏回归技术。所提出的检验方法可用于评估经典稠密因子回归模型相对于在因子回归中加入异质性冲击的"稀疏+稠密"备择模型的适用性。我们的检验无需调整参数、无需估计协方差矩阵，且实现简单。我们在时间序列依赖框架下从理论上建立了该检验的有效性。通过仿真实验，我们展示了该方法在有限样本下的优越表现。此外，利用FRED-MD数据集进行实证分析发现：当因变量为通货膨胀时，经典因子回归模型被拒绝；而当因变量为工业生产时则未被拒绝。这些发现为高维数据集选择合适模型提供了重要启示。