For example, U-MIDAS for DEF equation has a residual standard error of 0.96, compared with 0.69 for ADL-MIDAS. There is not much difference between one or two autoregressive lags. The standard error for ADL-MIDAS of the same form is 1.03 for one or two autoregressive lags. For example, unrestricted U-MIDAS for GDP has a residual standard error of 1.39. Comparison with MIDAS regression results indicate an improvement in fit because of autoregressive lags. Although, it is theoretically feasible, there may be some complications related to nonlinear estimation (an example here is the DEF equation with beta weights for monthly indicators and with two autoregressive lags). Models with one and two lags are given here. The MIDAS model can be extended to include autoregressive terms ( Ghysels and Marcellino, 2018).
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