This paper studies time series extrinsic regression (TSER): a regression task of which the aim is to learn the relationship between a time series and a continuous scalar variable; a task closely related to time series classification (TSC), which aims to learn the relationship between a time series and a categorical class label. This task generalizes time series forecasting, relaxing the requirement that the value predicted be a future value of the input series or primarily depend on more recent values. In this paper, we motivate and study this task, and benchmark existing solutions and adaptations of TSC algorithms on a novel archive of 19 TSER datasets which we have assembled. Our results show that the state-of-the-art TSC algorithm Rocket, when adapted for regression, achieves the highest overall accuracy compared to adaptations of other TSC algorithms and state-of-the-art machine learning (ML) algorithms such as XGBoost, Random Forest and Support Vector Regression. More importantly, we show that much research is needed in this field to improve the accuracy of ML models. We also find evidence that further research has excellent prospects of improving upon these straightforward baselines.

本文研究时间序列外在回归（TSER）：一种回归任务，其目的是学习时间序列和连续标量变量之间的关系；与时间序列分类（TSC）密切相关的任务，旨在学习时间序列和分类类标签之间的关系。此任务概括了时间序列预测，放宽了预测值是输入序列的未来值或主要取决于更新的值的要求。在本文中，我们激励和研究了这项任务，并在我们收集的 19 个 TSER 数据集的新档案中对现有的解决方案和 TSC 算法的适应进行了基准测试。我们的结果表明，最先进的 TSC 算法 Rocket 在适用于回归时，与其他 TSC 算法和最先进的机器学习 (ML) 算法（例如 XGBoost、随机森林和支持向量回归）的适配相比，它实现了最高的整体准确度。更重要的是，我们表明需要在该领域进行大量研究以提高 ML 模型的准确性。我们还发现证据表明，进一步的研究在这些简单的基线上具有很好的改进前景。