Improved Breitung and Roling estimator for mixed-frequency models with application to forecasting inflation rates

Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588-603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth SLS1) for estimating mixed-frequency models. This SLS1 approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in SLS1 solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator (SLS2). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of SLS2, compared to that of SLS1. Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed SLS2 estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R-2, which in turn leads to better forecasts.