Mixed frequency models with MA components

Temporal aggregation in general introduces a moving-average (MA) component in the aggregated model. A similar feature emerges when not all but only a few variables are aggregated, which generates a mixed-frequency (MF) model. The MA component is generally neglected, likely to preserve the possibility of ordinary least squares estimation, but the consequences have never been properly studied in the MF context. In this paper we show, analytically, in Monte Carlo simulations and in a forecasting application on US macroeconomic variables, the relevance of considering the MA component in MF mixed-data sampling (MIDAS) and unrestricted MIDAS models (MIDAS-autoregressive moving average (ARMA) and UMIDAS-ARMA). Specifically, the simulation results indicate that the short-term forecasting performance of MIDAS-ARMA and UMIDAS-ARMA are better than that of, respectively, MIDAS and UMIDAS. The empirical applications on nowcasting US gross domestic product (GDP) growth, investment growth, and GDP deflator inflation confirm this ranking. Moreover, in both simulation and empirical results, MIDAS-ARMA is better than UMIDAS-ARMA.