Online learning and forecast combination in unbalanced panels

This article evaluates the performance of a few newly proposed online forecast combination algorithms and compares them with some of the existing ones including the simple average and that of Bates and Granger (1969). We derive asymptotic results for the new algorithms that justify certain established approaches to forecast combination including trimming, clustering, weighting, and shrinkage. We also show that when implemented on unbalanced panels, different combination algorithms implicitly impute missing data differently, so that the performance of the resulting combined forecasts are not comparable. After explicitly imputing the missing observations in the U.S. Survey of Professional Forecasters (SPF) over 1968 IV-2013 I, we find that the equally weighted average continues to be hard to beat, but the new algorithms can potentially deliver superior performance at shorter horizons, especially during periods of volatility clustering and structural breaks.