This paper proposes two consistent in-sample model selection procedures for factor-augmented regressions in finite samples. We first demonstrate that the usual cross-validation is inconsistent, but that a generalization, leave-d-out cross-validation, selects the smallest basis for the space spanned by the true latent factors. The second proposed criterion is a generalization of the bootstrap approximation of the squared error of prediction from Shao (1996) to factor-augmented regressions. We show that these procedures are consistent model selection approaches. Simulation evidence documents improvements in the probability of selecting the smallest set of estimated factors than the usually available methods. An illustrative empirical application that analyzes the relationship between stock market excess returns and factors extracted from a large panel of U.S. macroeconomic and financial data is conducted. Our new procedures select factors that correlate heavily with interest rate spreads and with the Fama−French factors. These factors have in-sample predictive power for excess returns.

中文翻译：

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具有估计因子的因子增强回归中的模型选择

本文为有限样本中的因子增强回归提出了两种一致的样本内模型选择程序。我们首先证明通常的交叉验证是不一致的，但泛化，留出交叉验证，为真实潜在因素所跨越的空间选择最小的基础。第二个建议的标准是将 Shao (1996) 的预测平方误差的 bootstrap 近似推广到因子增强回归。我们表明这些程序是一致的模型选择方法。与通常可用的方法相比，模拟证据记录了选择最小估计因素集的概率的改进。进行了一个说明性的实证应用，分析了股票市场超额收益与从大量美国宏观经济和金融数据中提取的因素之间的关系。我们的新程序选择与利差和 Famaâˆ'French 因子密切相关的因子。这些因素对超额收益具有样本内预测能力。