中国人民大学

　　中国人民大学统计学院邀请宾夕法尼亚州立大学统计系薛凌洲作了题为“Sufficient Forecasting Using Factor Models(充分利用预测模型的因子)”的讲座。中国人民大学统计学院应用统计学科布局不仅深入经济社会发展领域和保险精算与金融风险管理领域，而且已经扩展到社会科学的许多领域如法律、新闻、政治学、伦理学、教育学、心理学、文献计量等领域之中，展示应用统计量化社会科学习究的重要作用。

　　当存在大量预测的和可能的非线性效应我们考虑预测的单一的时间序列。维首先通过高维(近似)的因素由主成分分析模型来实现降低。使用提取的因素，我们开发名为足够预测了一种新的预测方法，它提供了一套充分的预测指标，从高维预测推断的，以提供更多的预测能力。投影主成分分析将被用于增强的推断因素精度被假定一个半参数(近似)因子模型时。我们的方法也可以适用于使用提取因子剖足够回归。 {足够预测和深学习架构之间的连接被明确说明。}的充分的预测正确估计的潜在因素的投影索引即使是在一个非参数预测功能的存在。所提出的方法通过缩合通过因子模型的剖信息扩展了足够的尺寸减少到高维制度。我们推导出对这些投影方向以及足够的预测指数的估算值跨越的中央子空间的估算渐近性质。进一步的研究表明估计的因素移动靶的多元回归自然的方法产生，实际上就属于这一核心子空间的线性估计。我们的方法与理论预测允许的数量比观测的数量较大。我们终于证明了足够的预测在两个模拟研究线性预测和预测宏观经济变量的实证研究改进。

　　原文：We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal component analysis. Using the extracted factors, we develop a novel forecasting method called the sufficient forecasting, which provides a set of sufficient predictive indices, inferred from high-dimensional predictors, to deliver additional predictive power. The projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi-parametric (approximate) factor model is assumed. Our method is also applicable to cross-sectional sufficient regression using extracted factors. {The connection between the sufficient forecasting and the deep learning architecture is explicitly stated.} The sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function. The proposed method extends the sufficient dimension reduction to high-dimensional regimes by condensing the cross-sectional information through factor models. We derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices. We further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace. Our method and theory allow the number of predictors to be larger than the number of observations. We finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables.