The study motivates the estimation problem of short dynamic panel data models in the presence of higher frequency regressors where it is required to weigh the regressor series to be at the same frequency of the dependent variable. With the focus on First Difference Generalized Method of Moments (DIF GMM) and System Generalized Method of Moments (SYS GMM) estimators, short dynamic panel data models were discussed extensively in two cases the first is the balanced case and the second is the mixed frequency case where there is a higher frequency regressor(s). The weighting of the higher frequency regressor can be carried out using Mixed Data Sampling (MIDAS). In the presence of a higher frequency regressor and by assuming AR (1) of the lower frequency time dimension as a data generating process for the regressor, the initial conditions satisfying mean stationarity required for SYS GMM MIDAS were derived. Mone Carlo simulations were carried out where the results showed that using SYS GMM MIDAS exploited more power than DIF GMM MIDAS. In addition, using the average for weighting as well as testing the significance of the higher frequency regressor parameter resulted in low power.