State Space Models and MIDAS Regressions

We examine the relationship between Mi(xed) Da(ta) S(ampling) (MIDAS) regressions and the Kalman filter when forecasting with mixed frequency data. In general, state space models involve a system of equations, whereas MIDAS regressions involve a single equation. As a consequence, MIDAS regressions might be less efficient, but could also be less prone to parameter estimation error and/or specification errors. We examine how MIDAS regressions and Kalman filters match up under ideal circumstances, that is in population, and in cases where all the stochastic processes—low and high frequency—are correctly specified. We characterize cases where the MIDAS regression exactly replicates the steady state Kalman filter weights. We compare MIDAS and Kalman filter forecasts in population where the state space model is misspecified. We also compare MIDAS and Kalman filter forecasts in small samples. The paper concludes with an empirical application. Overall we find that the MIDAS and Kalman filter methods give similar forecasts. In most cases, the Kalman filter is a bit more accurate, but it is also computationally much more demanding.