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.

中文翻译：

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具有函数系数的非线性因子增强预测回归模型

本文介绍了一类新的函数系数预测回归模型，其中回归量由自回归量和潜在因子回归量组成，系数随特定指标变量而变化。通过对高维外生变量施加近似因子模型并随后实施经典主成分分析来估计不可观察因子回归量。使用估计的因子回归量，使用局部线性平滑方法估计系数函数（适当旋转）并获得响应变量的一步超前非线性预测，然后引入wild bootstrap程序构建预测区间. 在正则条件下，推导出所提出方法的渐近性质，表明使用估计因子回归量的局部线性估计量和非线性预测与使用真实潜在因子回归量的那些渐近等效。开发的模型和方法进一步推广到具有函数系数的因子增强向量预测回归。最后，给出了一些广泛的模拟研究和预测英国通货膨胀的实证应用，以检验所提出的模型和方法的有限样本性能。