Quantile regression models with factor‐augmented predictors and information criterion

For situations with a large number of series, N, each with T observations and each containing a certain amount of information for prediction of the variable of interest, we propose a new statistical modelling methodology that first estimates the common factors from a panel of data using principal component analysis and then employs the estimated factors in a standard quantile regression. A crucial step in the model‐building process is the selection of a good model among many possible candidates. Taking into account the effect of estimated regressors, we develop an information‐theoretic criterion. We also investigate the criterion when there is no estimated regressors. Results of Monte Carlo simulations demonstrate that the proposed criterion performs well in a wide range of situations.