Time series forecasting is an important and forefront task in many real-world
applications. However, most of time series forecasting techniques assume that
the training data is clean without anomalies. This assumption is unrealistic
since the collected time series data can be contaminated in practice. The
forecasting model will be inferior if it is directly trained by time series
with anomalies. Thus it is essential to develop methods to automatically learn
a robust forecasting model from the contaminated data. In this paper, we first
statistically define three types of anomalies, then theoretically and
experimentally analyze the loss robustness and sample robustness when these
anomalies exist. Based on our analyses, we propose a simple and efficient
algorithm to learn a robust forecasting model. Extensive experiments show that
our method is highly robust and outperforms all existing approaches. The code
is available at this https URL

时间序列预测是许多实际应用中的重要任务，但大部分时间序列预测技术都假设训练数据是没有异常值的。然而，在实践中，由于采集到的时间序列数据可能受到污染，这个假设是不现实的。因此，有必要开发方法从受到污染的数据中自动学习出一个鲁棒的预测模型。本文首先从统计视角定义了三种异常值，然后在这些异常值存在时进行了理论和实验分析损失稳健性和样本稳健性。基于我们的分析，我们提出了一种简单高效的算法来学习鲁棒的预测模型。大量实验证明我们的方法具有很高的稳健性，并且优于现有的所有方法。