A Predictive Approach for Selection of Diffusion Index Models

In this article, we propose a predictive mean squared error criterion for selecting diffusion index models, which are useful in forecasting when many predictors are available. A special feature of the proposed criterion is that it takes into account the uncertainty in estimated common factors. The new criterion is based on estimating the predictive mean squared error in forecasting with correction for asymptotic bias. The resulting estimate of bias-corrected forecast-error is shown to be <inline-formula> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="lecr_a_807105_o_ilm0001.gif"/> </inline-formula> consistent. The proposed criterion is a natural extension of the traditional Akaike information criterion (AIC), but it does not require the distributional assumptions for the likelihood. Results of real data analysis and Monte Carlo simulations demonstrate that the proposed criterion works well in comparison with the commonly used AIC and Bayesian information criteria.