Forecast combination involves using multiple forecasts to create a single, more accurate prediction. Recently, feature-based forecasting has been employed to either select the most appropriate forecasting models or to optimize the weights of their combination. In this paper, we present a multi-task optimization paradigm that focuses on solving both problems simultaneously and enriches current operational research approaches to forecasting. In essence, it incorporates an additional learning and optimization task into the standard feature-based forecasting approach, focusing on the identification of an optimal set of forecasting methods. During the training phase, an optimization model with linear constraints and quadratic objective function is employed to identify accurate and diverse methods for each time series. Moreover, within the training phase, a neural network is used to learn the behavior of that optimization model. Once training is completed the candidate set of methods is identified using the network. The proposed approach elicits the essential role of diversity in feature-based forecasting and highlights the interplay between model combination and model selection when optimizing forecasting ensembles. Experimental results on a large set of series from the M4 competition dataset show that our proposal enhances point forecast accuracy compared to state-of-the-art methods.

翻译：预测组合是指利用多种预测方法生成单一且更准确的预测结果。近年来，基于特征的预测方法已被用于选择最合适的预测模型或优化其组合权重。本文提出了一种多任务优化范式，旨在同时解决这两个问题，并丰富了当前运筹学在预测领域的研究方法。本质上，该方法在标准特征预测框架中引入了一个额外的学习与优化任务，专注于识别最优预测方法集。在训练阶段，采用具有线性约束和二次目标函数的优化模型，为每个时间序列识别准确且多样化的预测方法。同时，在训练阶段利用神经网络学习该优化模型的行为。训练完成后，通过该网络识别候选方法集。所提方法揭示了多样性在特征预测中的关键作用，并阐明了模型组合与模型选择在优化预测集成时的相互作用。在M4竞赛数据集的大量序列上进行的实验结果表明，与现有最先进方法相比，我们的方法提升了点预测的准确性。