Solving the Forecast Combination Puzzle Using Double Shrinkages*

Abstract

This study develops a new approach that shrinks the forecast combination weights towards equal weights by using weighted least squares and towards zero weight by using regularization constraints. We reveal the significant predictability of excess returns to the S&P500 index that can be achieved by using this double shrinkage combination (DSC). Furthermore, our DSC approach significantly outperforms the naïve equal-weighted combination, solving the combination puzzle. The equal-weight shrinkage has greater effect in economic recessions, whereas the zero-weight shrinkage dominates in economic expansions. The DSC's superior performance over that of the naïve combination is observed in the application of forecasting macroeconomic indicators.