Sufficient forecasting using factor models

Abstract

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.

High-dimensional factor model and its applications to statistical machine learning

“…多指标模型通过 多个因子线性组合 (文献 [16] 称它为扩散指标, diffusion indices) 去预测 Y . 文献 [121] 详细研究了多 指标模型 [122,123] 对多指标模型的研究开始, 至今有关扩散指标的研究已经有了很大发展, 详情参见文献 [124,125] 及其 参考文献.…”

The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications

“…By addressing estimation and inference in an interesting high-dimensional factor augmented regression model appropriate for panel data, our article complements the large factor model literature and the rapidly growing literature dealing with obtaining valid inferential statements following regularized estimation. See, for example, Bai (2003), Bai and Ng (2002), Stock and Watson (2002), and Fan, Xue, and Yao (2017) for fundamental references on factor models in econometrics and Bai and Ng (2006) and Bernanke, Boivin, and Eliasz (2005) for factor augmented regression. For approaches to obtaining valid inferential statements in a variety of different high-dimensional settings, see, for example, Belloni, Chen, Chernozhukov, and Hansen (2012), Belloni, Chernozhukov, Fernández-Val, and Hansen (2017), Belloni, Chernozhukov, and Hansen (2014), Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, and Newey (2016), Dezeure, Bühlmann, and Zhang (2017), Fan and Li (2001), van de Geer, Bühlmann, Ritov, and Dezeure (2014), Wager and Athey (2017), and Zhang and Zhang (2014).…”

Posterior Consistency of Factor Dimensionality in High-Dimensional Sparse Factor Models

“…That is, the distribution of Y is determined by the structured covariance matrix BB + σ 2 I. This decomposition of the covariance matrix leads to the substantial reduction of the model complexity, and thus the factor model has been applied to a broad range of areas including high-dimensional covariance estimation (Fan et al, 2008(Fan et al, , 2011(Fan et al, , 2018, high-dimensional supervised learning (Fan et al, 2017;Kneip and Sarda, 2011;Silva, 2011;Stock and Watson, 2002) and multiple testing under arbitrary dependence (Fan et al, 2012(Fan et al, , 2019Leek and Storey, 2008), and popularly used in various application fields such as economy, psychology and gene expression studies (e.g., Bernanke et al, 2005;Carvalho et al, 2008;Forni et al, 2003;Hochreiter et al, 2006;McCrae and John, 1992).…”