科学研究

Dr. Yuhong Yang is Professor at Yau Mathematical Sciences Center. He received his Ph.D. in statistics from Yale University in 1996. His research interests include model selection, model averaging, multi-armed bandit problems, causal inference, high-dimensional data analysis, and machine learning. He has published in journals in several fields including Annals of Statistics, JASA, IEEE Transactions on Information Theory, IEEE Signal Processing Magazine, Journal of Econometrics, Journal of Machine Learning Research, and International Journal of Forecasting. He is a recipient of the US NSF CAREER Award and a fellow of the Institute of Mathematical Statistics. He is included in the list of top 2% of the world's most cited scientists by Stanford University.

Forecast combination, initiated by Nobel Laureate Clive Granger, has proven to be a powerful tool for accurate prediction. However, there is an unresolved puzzle in the research area. It is often reported in the forecast combination literature that a simple average of candidate forecasts is more robust than sophisticated combining methods. This phenomenon is usually referred to as the “forecast combination puzzle”. What is really going on here?

We will examine the puzzle in a larger scope from multiple perspectives, including combination versus selection and different goals of forecast combination. In particular, we will review the $\ell_q$-aggregation of predictions and present theoretical understandings on potentials and prices to pay for different ways to combine candidate procedures. Based on our new understandings, both simulations and real data evaluations are conducted to illustrate the causes of the puzzle. We further propose a multi-level AFTER strategy that can integrate the strengths of different combining methods and adapt intelligently to the underlying scenario behind the data.