Nonlinear Factor‐Augmented Predictive Regression Models with Functional Coefficients

This article introduces a new class of functional‐coefficient predictive regression models, where the regressors consist of auto‐regressors and latent factor regressors, and the coefficients vary with certain index variable. The unobservable factor regressors are estimated through imposing an approximate factor model on high dimensional exogenous variables and subsequently implementing the classical principal component analysis. With the estimated factor regressors, a local linear smoothing method is used to estimate the coefficient functions (with appropriate rotation) and obtain a one‐step ahead nonlinear forecast of the response variable, and then a wild bootstrap procedure is introduced to construct the prediction interval. Under regularity conditions, the asymptotic properties of the proposed methods are derived, showing that the local linear estimator and the nonlinear forecast using the estimated factor regressors are asymptotically equivalent to those using the true latent factor regressors. The developed model and methodology are further generalized to the factor‐augmented vector predictive regression with functional coefficients. Finally, some extensive simulation studies and an empirical application to forecast the UK inflation are given to examine the finite‐sample performance of the proposed model and methodology.