英文文献：On the Selection of Common Factors for Macroeconomic Forecasting-论宏观经济预测常用因素的选择
英文文献作者：Alessandro Giovannelli,Tommaso Proietti
英文文献摘要：
We address the problem of selecting the common factors that are relevant for forecasting macroeconomic variables. In economic forecasting using diffusion indexes the factors are ordered, according to their importance, in terms of relative variability, and are the same for each variable to predict, i.e. the process of selecting the factors is not supervised by the predictand. We propose a simple and operational supervised method, based on selecting the factors on the basis of their significance in the regression of the predictand on the predictors. Given a potentially large number of predictors, we consider linear transformations obtained by principal components analysis. The orthogonality of the components implies that the standard t-statistics for the inclusion of a particular component are independent, and thus applying a selection procedure that takes into account the multiplicity of the hypotheses tests is both correct and computationally feasible. We focus on three main multiple testing procedures: Holm’s sequential method, controlling the family wise error rate, the Benjamini-Hochberg method, controlling the false discovery rate, and a procedure for incorporating prior information on the ordering of the components, based on weighting the p-values according to the eigenvalues associated to the components. We compare the empirical performances of these methods with the classical diffusion index (DI) approach proposed by Stock and Watson, conducting a pseudo-real time forecasting exercise, assessing the predictions of 8 macroeconomic variables using factors extracted from an U.S. dataset consisting of 121 quarterly time series. The overall conclusion is that nature is tricky, but essentially benign: the information that is relevant for prediction is effectively condensed by the first few factors. However, variable selection, leading to exclude some of the low order principal components, can lead to a sizable improvement in forecasting in specific cases. Only in one instance, real personal income, we were able to detect a significant contribution from high order components.

我们解决了选择与预测宏观经济变量相关的公共因素的问题。在使用扩散指标进行经济预测时，根据各因素的重要性和相对可变性，对每个要预测的变量进行排序，即选择因素的过程不受预测者的监督。我们提出了一种简单易行的监督方法，即根据预测回归和预测因子的显著性来选择影响因素。给定潜在的大量预测器，我们考虑由主成分分析得到的线性变换。组成部分的正交性意味着标准的t统计数据包含一个特定的组成部分是独立的，因此应用一个选择程序，考虑到假设检验的多重性是正确的和计算上可行的。我们专注于三个主要多个测试步骤:河中沙洲的序贯法,控制家庭明智的错误率,Benjamini-Hochberg方法,控制错误发现率,和合并过程组件的订购信息之前,基于加权假定值根据特征值相关的组件。我们将这些方法的实证性能与Stock和Watson提出的经典扩散指数(DI)方法进行了比较，进行了一个伪实时预测练习，评估了8个宏观经济变量的预测，这些预测使用的因素提取自一个包含121个季度时间序列的美国数据集。总的结论是，自然是棘手的，但本质上是良性的:与预测相关的信息被前几个因素有效地压缩了。然而，变量的选择，导致排除了一些低阶主成分，可以导致在特定的情况下有一个相当大的改善预测。只有在一个实例中，即真实的个人收入，我们能够检测出高阶成分的显著贡献。