  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 https://github.com/haochenglouis/RobustTSF.
