Fast RobustSTL: Efficient and Robust Seasonal-Trend Decomposition for Time Series with Complex Patterns

Many real-world time series data exhibit complex patterns with trend, seasonality, outlier and noise. Robustly and accurately decomposing these components would greatly facilitate time series tasks including anomaly detection, forecasting and classification. RobustSTL is an effective seasonal-trend decomposition for time series data with complicated patterns. However, it cannot handle multiple seasonal components properly. Also it suffers from its high computational complexity, which limits its usage in practice. In this paper, we extend RobustSTL to handle multiple seasonality. To speed up the computation, we propose a special generalized ADMM algorithm to perform the decomposition efficiently. We rigorously prove that the proposed algorithm converges approximately as standard ADMM while reducing the complexity from O(N2) to O(N log N) for each iteration. We empirically study our proposed algorithm with other state-of-the-art seasonal-trend decomposition methods, including MSTL, STR, TBATS, on both synthetic and real-world datasets with single and multiple seasonality. The experimental results demonstrate the superior performance of our decomposition algorithm in terms of both effectiveness and efficiency.