Solving the Forecast Combination Puzzle Using Double Shrinkages*
提出一种双重收缩方法，通过加权最小二乘向等权重收缩、通过正则化向零权重收缩，显著提升标普500指数超额收益的可预测性，并优于简单等权组合，解决了预测组合难题。
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.