  Extracting the underlying trend signal is a crucial step to facilitate time
series analysis like forecasting and anomaly detection. Besides noise signal,
time series can contain not only outliers but also abrupt trend changes in
real-world scenarios. To deal with these challenges, we propose a robust trend
filtering algorithm based on robust statistics and sparse learning.
Specifically, we adopt the Huber loss to suppress outliers, and utilize a
combination of the first order and second order difference on the trend
component as regularization to capture both slow and abrupt trend changes.
Furthermore, an efficient method is designed to solve the proposed robust trend
filtering based on majorization minimization (MM) and alternative direction
method of multipliers (ADMM). We compared our proposed robust trend filter with
other nine state-of-the-art trend filtering algorithms on both synthetic and
real-world datasets. The experiments demonstrate that our algorithm outperforms
existing methods.
