关键词: L1和L2规则化趋势滤波, Huber损失函数, Berhu罚函数, 稳健集成

Abstract: Huber loss function is a useful tool in robust regression, and Berhu penalty function is a hybrid of L1 and L2 penalty functions. In order to extract trend from time series with outliers, this paper proposes a robust hybrid of L1 and L2 regularized trend filtering based on Huber loss function and Berhu penalty function. This method is not sensitive to outliers and possesses advantages of L1 and L2 penalty function. Simulation analysis shows that when the time series have outliers and potential trend is unknown, robust hybrid method is a good compromise to give a better estimation. The method can be applied to financial data.

Key words: L1 and L2 regularized trend filtering, Huber loss function, Berhu Penalty Function, Robust Hybrid Method