The effects of temporal aggregation on MIDAS regressions

Abstract

Time series used in practice are often temporal aggregates. A MIDAS regression model may be fitted wrongly assuming the independent variables are not aggregated when in fact they are. We derive the correct model’s specification under temporal aggregation of the independent variables, thus identifying the correct number of dynamic terms and the order of the MA component. We also show that these depend on the frequency of the variables and the aggregation order used. As a result, the three alternative estimators considered are asymptotically biased and it is possible to rank them according to their bias in some cases. Our results are also confirmed by Monte Carlo experiments and are illustrated with an empirical application.