A Machine Learning Approach to the Forecast Combination Puzzle

Forecast combination algorithms provide a robust solution to noisy data and shifting process dynamics. However in practice, sophisticated combination methods often fail to consistently outperform the simple mean combination. This "forecast combination puzzle" limits the adoption of alternative com- bination approaches and forecasting algorithms by policy-makers. Through an adaptive machine learning algorithm designed for streaming data, this pa- per proposes a novel time-varying forecast combination approach that retains distribution-free guarantees in performance while automatically adapting com- binations according to the performance of any selected combination approach or forecaster. In particular, the proposed algorithm offers policy-makers the ability to compute the worst-case loss with respect to the mean combination ex-ante, while also guaranteeing that the combination performance is never worse than this explicit guarantee. Theoretical bounds are reported with re- spect to the relative mean squared forecast error. Out-of-sample empirical performance is evaluated on the Stock and Watson seven-country dataset and the ECB Sur- vey of Professional Forecasters.