Nonparametric Estimation of Sufficient Forecasting with a Diverging Number of Factors

Open Access
Yu, Xiufan
Graduate Program:
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 29, 2019
Committee Members:
  • Runze Li, Thesis Advisor/Co-Advisor
  • Lingzhou Xue, Thesis Advisor/Co-Advisor
  • Bing Li, Committee Member
  • Ephraim Mont Hanks, Committee Member
  • factor model
  • forecasting
  • principal components
  • high-dimensional predictors
  • nonparametric estimation
  • predictive inference
The sufficient forecasting (Fan, Xue and Yao, 2017) provides an effective forecasting procedure to estimate sufficient indices from high-dimensional predictors in the presence of a possible nonlinear forecast function. In this paper, we first revisit the sufficient forecasting and explore its underlying connections to Fama-Macbeth regression and partial least squares. Then, we develop an inferential theory of sufficient forecasting within the high-dimensional framework with large cross sections, a large time dimension and a diverging number of factors. We derive the rate of convergence of the estimated factors and loadings and characterize the asymptotic behavior of the estimated sufficient forecasting directions without requiring the restricted linearity condition. The predictive inference of the estimated nonparametric forecasting function is obtained with nonparametrically estimated sufficient indices. We further demonstrate the power of the sufficient forecasting in an empirical study of financial markets.