Yet another look at MIDAS regression

A MIDAS regression involves a dependent variable observed at a low frequency and independent variables observed at a higher frequency. This paper relates a true high frequency data generating process, where also the dependent variable is observed (hypothetically) at the high frequency, with a MIDAS regression. It is shown that a correctly specified MIDAS regression usually includes lagged dependent variables, a substantial number of explanatory variables (observable at the low frequency) and a moving average term. Next, the parameters of the explanatory variables unlikely obey certain convenient patterns, and hence imposing such restrictions in practice is not recommended.