Combining forecasts from multiple experts often yields more accurate results than relying on a single expert. In this paper, we introduce a novel regularized ensemble method that extends the traditional linear opinion pool by leveraging both current forecasts and historical performances to set the weights. Unlike existing approaches that rely only on either the current forecasts or past accuracy, our method accounts for both sources simultaneously. It learns weights by minimizing the variance of the combined forecast (or its transformed version) while incorporating a regularization term informed by historical performances. We also show that this approach has a Bayesian interpretation. Different distributional assumptions within this Bayesian framework yield different functional forms for the variance component and the regularization term, adapting the method to various scenarios. In empirical studies on Walmart sales and macroeconomic forecasting, our ensemble outperforms leading benchmark models both when experts' full forecasting histories are available and when experts enter and exit over time, resulting in incomplete historical records. Throughout, we provide illustrative examples that show how the optimal weights are determined and, based on the empirical results, we discuss where the framework's strengths lie and when experts' past versus current forecasts are more informative.

翻译：整合多位专家的预测结果通常比依赖单一专家获得更准确的预测。本文提出一种新颖的正则化集成方法，该方法通过同时利用当前预测与历史表现来设置权重，从而扩展了传统的线性意见池。与现有仅依赖当前预测或过去准确性的方法不同，我们的方法同时考虑了这两种信息源。该方法通过最小化组合预测（或其变换形式）的方差来学习权重，同时引入由历史表现信息构成的正则化项。我们还证明了该方法具有贝叶斯解释。在此贝叶斯框架下，不同的分布假设会对方差项与正则化项产生不同的函数形式，从而使方法能适应多种场景。在沃尔玛销售数据与宏观经济预测的实证研究中，无论专家拥有完整预测历史记录，还是在专家随时间动态加入与退出的不完整历史记录情况下，我们的集成方法均优于主流基准模型。通过示例，我们展示了最优权重的确定过程，并基于实证结果讨论了该框架的优势所在，以及专家历史预测与当前预测在不同情境下的信息价值。