Inverse Moment methods for Sufficient Forecasting using High-Dimensional Predictors

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