Quantile regression models with factor-augmented predictors and information criterion

For situations with a large number of series,N, each withTobservations 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.