We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time series dependence and polynomial tails. We outline a data-driven rule to select the tuning parameter and prove its theoretical validity. In simulation experiments, our procedure exhibits high power against sparse alternatives and low power against dense deviations from the null. Moreover, we apply our test to various datasets in macroeconomics and finance and often reject the null. This suggests the presence of sparsity -- on top of a dense model -- in commonly studied economic applications. The R package FAS implements our approach.

翻译：本文提出了一种新颖的自举检验方法，用于检验稠密模型（即因子回归）与包含稀疏异质性成分的“稀疏+稠密”增强替代模型。该检验的渐近性质在时间序列依赖性和多项式尾部条件下得以建立。我们提出了一种数据驱动的规则来选择调优参数，并证明了其理论有效性。在仿真实验中，我们的方法对稀疏替代假设展现出较高的检验功效，而对偏离原假设的稠密备择假设则功效较低。此外，我们将该检验应用于宏观经济学和金融学的多个数据集，结果经常拒绝原假设。这表明在常见的经济学应用研究中，除了稠密模型外，还存在稀疏性特征。R软件包FAS实现了本文方法。