A Robust and Efficient Multi-Scale Seasonal-Trend Decomposition
This work addresses a domain-specific problem for time series analysis in applications like forecasting and anomaly detection, offering an incremental improvement over existing decomposition methods.
The paper tackles the problem of decomposing time series with multiple seasonality, which is computationally expensive and data-intensive for existing methods, by proposing a multi-scale algorithm that uses down-sampling and optimization to achieve accurate results with significantly improved efficiency.
Many real-world time series exhibit multiple seasonality with different lengths. The removal of seasonal components is crucial in numerous applications of time series, including forecasting and anomaly detection. However, many seasonal-trend decomposition algorithms suffer from high computational cost and require a large amount of data when multiple seasonal components exist, especially when the periodic length is long. In this paper, we propose a general and efficient multi-scale seasonal-trend decomposition algorithm for time series with multiple seasonality. We first down-sample the original time series onto a lower resolution, and then convert it to a time series with single seasonality. Thus, existing seasonal-trend decomposition algorithms can be applied directly to obtain the rough estimates of trend and the seasonal component corresponding to the longer periodic length. By considering the relationship between different resolutions, we formulate the recovery of different components on the high resolution as an optimization problem, which is solved efficiently by our alternative direction multiplier method (ADMM) based algorithm. Our experimental results demonstrate the accurate decomposition results with significantly improved efficiency.