Abstract

Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weakly serially dependent, and the sample size be fairly large, although in practical applications, one or several of these conditions may fail. In these cases, it is difficult to analyze the eigenvectors of the data matrix. To address this issue, we propose simple estimators of the latent factors using cross-sectional projections of the panel data, by weighted averages with predetermined weights. These weights are chosen to diversify away the idiosyncratic components, resulting in “diversified factors.” Because the projections are conducted cross-sectionally, they are robust to serial conditions, easy to analyze and work even for finite length of time series. We formally prove that this procedure is robust to over-estimating the number of factors, and illustrate it in several applications, including post-selection inference, big data forecasts, large covariance estimation, and factor specification tests. We also recommend several choices for the diversified weights. Supplementary materials for this article are available online.

摘要

因子模型的估计和应用往往依赖于潜在因子的数量是一致估计的关键条件，这反过来又要求因子相对较强，数据是平稳的和弱序列依赖，样本量相当大，尽管在实际应用中，这些条件中的一种或几种可能会失效。在这些情况下，很难分析数据矩阵的特征向量。为了解决这个问题，我们使用面板数据的横截面投影，通过具有预定权重的加权平均值，提出了潜在因素的简单估计。选择这些权重是为了分散特殊成分，从而产生“多样化的因素”。因为投影是横截面进行的，所以它们对连续条件是稳健的，即使对于有限长度的时间序列，也易于分析和工作。我们正式证明了这个过程对于高估因子数量是稳健的，并在几个应用中进行了说明，包括选择后推理、大数据预测、大协方差估计和因子规范测试。我们还为多样化的权重推荐了几种选择。本文的补充材料可在线获取。