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：本研究提出一种基于自助法的检验方法，用于评估高维因子增强稀疏回归模型中因子回归的有效性。该模型融合了因子回归与稀疏回归技术。该检验可评估经典稠密因子回归模型相较于在因子回归基础上加入异质冲击的稀疏加稠密备择模型的适用性。我们提出的检验无需调优参数，无需估计协方差矩阵，且实现简便。在时间序列依赖条件下，该检验的有效性得到了理论证明。通过模拟实验，我们展示了该方法在有限样本下的优良表现。此外，利用FRED-MD数据集应用该检验，我们发现当因变量为通胀指标时，经典因子回归模型被拒绝，而因变量为工业生产指标时则未被拒绝。这些发现为高维数据集选择合适模型提供了见解。