TS3Net: Triple Decomposition with Spectrum Gradient for Long-Term Time Series Analysis

Time series analysis has a wide range of applications in the fields of weather forecasting, traffic management, fault detection, intelligent operation, etc. In the real world, time series typically consist of dynamic fluctuations and mixtures of periodicities, which bring challenges on modeling and analyzing their patterns. To overcome the complexities, a common approach is to decompose long-term time series into sub-components for easier analysis. Unlike conventional time series decomposition that decouples a series into the trend and seasonal parts, we proposed a novel triple decomposition method to decouple a long-term series into three components: trend-part, regular-part, and fluctuant-part. Notably, the third part is a particular component that represents the dynamic spectral fluctuation in time series with the formulation of spectrum gradient. Based on triple decomposition, we propose a novel task-general deep learning model called TS3Net for long-term series analysis. It introduces a temporal-frequency block (TF-Block) with a multi-branch structure to expand the time series into a 2D temporal-frequency distribution. Subsequently, deep representation can be learned by a vision architecture that captures the dynamic variations from the complex multi-periodic series. The decomposed components are processed by TS3Net individually, and their results are integrated to form the final result for time series analysis. We conduct extensive experiment based on six open datasets to evaluate the proposed method in comparison with 10 baselines. Numerical results show that TS3Net significantly outperforms the state-of-the-art methods on both time series forecasting and imputation tasks. The source codes of TS3Net are publicly available on https://github.com/Xiang-Kai/TS3Net.