The time averaging of the high-frequency variable is a traditional approach to have the mixed frequency variables in one regression model. Mixed data sampling (MIDAS) regression models are proposed as an alternative, as time averaging may omit some crucial information in the high-frequency variable. However, if the time averaging is good enough, the nonlinear estimation involved in the MIDAS estimation can be avoided. In this paper, based on a Durbin-Wu-Hausman type test, we propose a specification test for time averaging models against the mixed data sampling regression model. In particular, a set of instruments is proposed and theoretically validated when the frequency ratio is large enough. This finding is supported in finite samples as well.