Depth-Weighted Forecast Combination: Application to COVID-19 Cases

We develop a novel forecast combination based on the order statistics of individual predictability when many forecasts are available. To this end, we define the notion of forecast depth, which measures the size of forecast errors during the training period and provides a ranking among different forecast models. The forecast combination is in the form of a depth-weighted trimmed mean, where the group of models with the worst forecasting performance during the training period is dropped. We derive the limiting distribution of the depth-weighted forecast combination, based on which we can readily construct forecast confidence intervals. Using this novel forecast combination, we forecast the national level of new COVID-19 cases in the U.S. and compare it with other approaches including the ensemble forecast from the Centers for Disease Control and Prevention. We find that the depth-weighted forecast combination yields more accurate predictions compared with other forecast combinations.