Model selection with estimated factors and idiosyncratic components
提出了一致性信息准则，用于选择同时包含大数据集中异质成分和共同因子成分的预测模型，解决了估计误差带来的选择不一致问题，并通过蒙特卡洛模拟和汇率预测应用验证了其有效性。
Summary This paper provides consistent information criteria for the selection of forecasting models that use a subset of both the idiosyncratic and common factor components of a big dataset. This hybrid model approach has been explored by recent empirical studies to relax the strictness of pure factor‐augmented model approximations, but no formal model selection procedures have been developed. The main difference to previous factor‐augmented model selection procedures is that we must account for estimation error in the idiosyncratic component as well as the factors. Our main contribution is to show the conditions required for selection consistency of a class of information criteria that reflect this additional source of estimation error. We show that existing factor‐augmented model selection criteria are inconsistent in circumstances where N is of larger order than , where N and T are the cross‐section and time series dimensions of the dataset respectively, and that the standard Bayesian information criterion is inconsistent regardless of the relationship between N and T . We therefore propose a new set of information criteria that guarantee selection consistency in the presence of estimated idiosyncratic components. The properties of these new criteria are explored through a Monte Carlo simulation study. The paper concludes with an empirical application to long‐horizon exchange rate forecasting using a recently proposed model with country‐specific idiosyncratic components from a panel of global exchange rates.