Forecasting Mixed-Frequency Time Series with ECM-MIDAS Models

This paper proposes a mixed‐frequency error correction model for possibly cointegrated non‐stationary time series sampled at different frequencies. We highlight the impact, in terms of model specification, of the choice of the particular high‐frequency explanatory variable to be included in the cointegrating relationship, which we call a dynamic mixed‐frequency cointegrating relationship. The forecasting performance of aggregated models and several mixed‐frequency regressions are compared in a set of Monte Carlo experiments. In particular, we look at both the unrestricted mixed‐frequency model and at a more parsimonious MIDAS regression. Whereas the existing literature has only investigated the potential improvements of the MIDAS framework for stationary time series, our study emphasizes the need to include the relevant cointegrating vectors in the non‐stationary case. Furthermore, it is illustrated that the choice of dynamic mixed‐frequency cointegrating relationship does not matter as long as the short‐run dynamics are adapted accordingly. Finally, the unrestricted model is shown to suffer from parameter proliferation for samples of relatively small size, whereas MIDAS forecasts are robust to over‐parameterization. We illustrate our results for the US inflation rate.