Inverse Moment Methods for Sufficient Forecasting Using High-Dimensional Predictors

21 Pages Posted: 1 May 2017 Last revised: 25 May 2021

See all articles by Wei Luo

Wei Luo

Zhejiang University

Lingzhou Xue

Pennsylvania State University - Department of Statistics

Jiawei Yao

Princeton University

Xiufan Yu

Pennsylvania State University - Department of Statistics

Date Written: March 31, 2021

Abstract

We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimated factors, to derive the reduced data for subsequent forecasting. Using directional regression and the inverse third-moment method in the stage of sufficient dimension reduction, the proposed methods can capture the non-monotone effect of factors on the response. We also allow a diverging number of factors and only impose general regularity conditions on the distribution of factors, avoiding the undesired time reversibility of the factors by the latter. These make the proposed methods fundamentally more applicable than the sufficient forecasting method in Fan et al. (2017). The proposed methods are demonstrated in both simulation studies and an empirical study of forecasting monthly macroeconomic data from 1959 to 2016. Also, our theory contributes to the literature of sufficient dimension reduction, as it includes an invariance result, a path to perform sufficient dimension reduction under the high-dimensional setting without assuming sparsity, and the corresponding order-determination procedure.

Keywords: factor model; forecasting; inverse moments; learning indices; principal components; regression; sufficient dimension reduction

JEL Classification: C13, C30, C33

Suggested Citation

Luo, Wei and Xue, Lingzhou and Yao, Jiawei and Yu, Xiufan, Inverse Moment Methods for Sufficient Forecasting Using High-Dimensional Predictors (March 31, 2021). Available at SSRN: https://ssrn.com/abstract=2961010 or http://dx.doi.org/10.2139/ssrn.2961010

Wei Luo

Zhejiang University ( email )

38 Zheda Road
Hangzhou, Zhejiang 310058
China

Lingzhou Xue (Contact Author)

Pennsylvania State University - Department of Statistics ( email )

326 Thomas Building
University Park, PA 16802
United States

Jiawei Yao

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Xiufan Yu

Pennsylvania State University - Department of Statistics ( email )

University Park, PA
United States

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