Regularized Ensemble Forecasting for Learning Weights from Historical and Current Forecasts

TL;DR

This paper presents a regularized ensemble forecasting method that combines current and historical expert forecasts, improving accuracy by adaptively learning weights with a Bayesian interpretation across different scenarios.

Contribution

It introduces a novel regularized ensemble approach that leverages both current and past forecast data, extending traditional methods with a Bayesian framework for adaptive weighting.

Findings

Outperforms benchmark models in Walmart sales and macroeconomic forecasting.

Effective with complete and incomplete historical data.

Demonstrates how to determine optimal weights based on empirical examples.

Abstract

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.