从多种投影中学习潜在因子及其对高估和弱因子的应用
Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors
摘要：
因子模型的估计和应用往往依赖于潜在因子数被一致估计这一关键条件，而这又要求因子相对较强、数据平稳且序列相关性较弱以及样本量相当大，尽管在实际应用中，这些条件中的一个或几个可能会失败。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，我们提出了简单的估计的潜在因素，使用横截面预测的面板数据，通过加权平均与预先确定的权重。选择这些权重是为了使特殊成分多样化，从而产生“多样化因素”。由于投影是在横截面上进行的，因此它们对序列条件具有鲁棒性，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是强大的高估的因素的数量，并说明它在几个应用程序，包括后选择推理，大数据预测，大协方差估计和因素规格测试。我们还推荐了多种多样的权重选择。
英文摘要：
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 weak serial dependence, 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 pre-determined 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.
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