In-Sample Inference and Forecasting in Misspecified Factor Models
研究了在存在大量外生预测变量的回归中，使用主成分、岭回归等四种降维方法进行样本内预测和样本外预测，推导了收敛速度，并基于交叉验证提出数据驱动的参数选择方法。蒙特卡洛模拟和美国通胀与产出增长预测应用表明，降维方法在多种场景下优于传统方法，并能有效应对预测能力的不稳定性。
This article considers in-sample prediction and out-of-sample forecasting in regressions with many exogenous predictors. We consider four dimension-reduction devices: principal components, ridge, Landweber Fridman, and partial least squares. We derive rates of convergence for two representative models: an ill-posed model and an approximate factor model. The theory is developed for a large cross-section and a large time-series. As all these methods depend on a tuning parameter to be selected, we also propose data-driven selection methods based on cross-validation and establish their optimality. Monte Carlo simulations and an empirical application to forecasting inflation and output growth in the U.S. show that data-reduction methods outperform conventional methods in several relevant settings, and might effectively guard against instabilities in predictors’ forecasting ability.