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Market-Based Solutions to Vital Economic Issues
Research
May 5, 2013

State Space Models and MIDAS Regressions

Abstract

We examine the relationship between MIDAS regressions and Kalman filter state space models applied to mixed frequency data. In general, the latter involves a system of equations, whereas in contrast MIDAS regressions involve a (reduced form) single equation. As a consequence, MIDAS regressions might be less efficient, but also less prone to specification errors. First 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 by a linear state space model. We characterize cases where the MIDAS regression exactly replicates the steady state Kalman filter weights. In cases where the MIDAS regression is only an approximation, we compute the approximation error and find it to be small (using two different metrics). Both in population and in small samples, we find that forecasts from MIDAS regressions are generally quite similar to those from the Kalman filter. Kalman filter forecasts are typically a little better, but MIDAS regressions can be more accurate if the state-space model is mis-specified or over-parameterized. The paper concludes with an empirical application comparing MIDAS and Kalman filtering to predict future GDP growth, using monthly macroeconomic series.

Note: Research papers posted on ResearchGate, including any findings, may differ from the final version chosen for publication in academic journals.


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