A Robust and Efficient Multi-Scale Seasonal-Trend Decomposition

TL;DR

This paper introduces a fast, multi-scale seasonal-trend decomposition method for complex time series with multiple seasonalities, improving accuracy and efficiency over existing approaches.

Contribution

The paper presents a novel multi-scale decomposition algorithm that efficiently handles multiple seasonalities by down-sampling and optimization, reducing computational costs.

Findings

Accurate decomposition of multi-seasonal time series.

Significant efficiency improvements over existing methods.

Effective handling of long periodic seasonal components.

Abstract

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.