Sufficient Forecasting Using Factor Models
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基于因子模型的充分预测
- 研究问题
- 当预测变量数量很大且预测关系可能非线性时，如何压缩信息并构造足以预测单一时间序列的低维指标？
- 方法与思路
- 作者先用主成分分析提取因子，再估计充分预测方向；在半参数因子设定下，利用投影主成分分析改善因子估计。
- 材料陈述的贡献
- 摘要称建立了中心子空间与预测指标的渐近理论，并在模拟和宏观变量预测应用中观察到相对线性预测的改善。
- 阅读关注点
- 全文应核对因子结构、中心子空间识别及维度增长条件，并检查非线性预测指标的估计步骤和预测比较设计。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或被期刊接收；摘要未说明完整理论条件及预测改善的具体幅度。
原文摘要
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.