This papers proposes a generic, high-level methodology for generating forecast combinations that would deliver the optimal linearly combined forecast in terms of the mean-squared forecast error if one had access to two population quantities: the mean vector and the covariance matrix of the vector of individual forecast errors. We point out that this problem is identical to a mean-variance portfolio construction problem, in which portfolio weights correspond to forecast combination weights. We allow negative forecast weights and interpret such weights as hedging over and under estimation risks across estimators. This interpretation follows directly as an implication of the portfolio analogy. We demonstrate our method's improved out-of-sample performance relative to standard methods in combining tree forecasts to form weighted random forests in 14 data sets.

翻译：本文提出了一种通用的高层方法论，用于生成预测组合，该方法能够在获取两个总体量（个体预测误差向量的均值向量和协方差矩阵）时，以均方预测误差为准则提供最优线性组合预测。我们指出该问题与均值-方差投资组合构建问题具有同构性，其中投资组合权重对应预测组合权重。我们允许负预测权重存在，并将此类权重解释为跨估计器对高估与低估风险的"对冲行为"。这一诠释直接源自投资组合分析的类比推论。通过在14个数据集中结合树预测形成加权随机森林的实证，我们证明了该方法相较于标准方法在样本外预测性能上的提升。