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. In this paper, we aim to develop methods to automatically learn a robust forecasting model from a data-centric perspective. Specifically, we first statistically define three types of anomalies in time series data, then theoretically and experimentally analyze the \emph{loss robustness} and \emph{sample robustness} when these anomalies exist. Based on our analyses, we propose a simple and efficient algorithm to learn a robust forecasting model which outperforms all existing approaches.