Group penalized unrestricted mixed data sampling model with application to forecasting US GDP growth

To identify important variables at block level in high dimensional mixed frequency data analysis, we introduce a specific type of group penalized function into the U-MIDAS regression framework, and propose a novel group penalized unrestricted MIDAS (GP-U-MIDAS) model. The GP-U-MIDAS model is able to take into account the grouping structures produced via the frequency alignment operation in U-MIDAS regressions. It performs both group selection and regularization in order to enhance its own interpretability and prediction ability. In Monte Carlo experiments, we find that the GP-U-MIDAS model is significantly superior to the P-U-MIDAS, FC-U-MIDAS and U-MIDAS models in terms of variable selection and prediction accuracy, when either all variables of a group are included or excluded. The superiority of GP-U-MIDAS model is also illustrated in a real-world application on forecasting US quarterly GDP growth. The empirical results show that the GP-U-MIDAS model outperforms the other competitive models, and is able to select crucial indicators, such as industrial production, personal consumption expenditures and so on, for GDP growth forecasts, which are especially useful for policy makers.