Forecasting Mixed Frequency Time Series with ECM-MIDAS Models

This paper proposes a mixed-frequency error-correction model in order to develop a regressionapproach for non-stationary variables sampled at different frequencies that are possiblycointegrated. We show that, at the model representation level, the choice of the timing betweenthe low-frequency ependent and the high-frequency explanatory variables to be included in thelong-run has an impact on the remaining dynamics and on the forecasting properties. Then, wecompare in a set of Monte Carlo experiments the forecasting performances of the low-frequencyaggregated model and several mixed-frequency regressions. In particular, we look at both theunrestricted mixed-frequency model and at a more parsimonious MIDAS regression. Whilst theexisting literature has only investigated the potential improvements of the MIDAS framework forstationary time series, our study emphasizes the need to include the relevant cointegratingvectors in the non-stationary case. Furthermore, it is illustrated that the exact timing of thelong-run relationship does notmatter as long as the short-run dynamics are adapted according to the composition of thedisequilibrium error. Finally, the unrestricted model is shown to suffer from parameterproliferation for small sample sizeswhereas MIDAS forecasts are robust to over-parameterization. Hence, the data-driven,low-dimensional and flexible weighting structure makes MIDAS a robust and parsimonious method tofollow when the true underlying DGP is unknown while still exploiting information present in thehigh-frequency. An empirical application illustrates the theoretical and the Monte Carlo results.