ST-Norm: Spatial and Temporal Normalization for Multi-variate Time Series Forecasting

Abstract

Multi-variate time series (MTS) data is a ubiquitous class of data abstraction in the real world. Any instance of MTS is generated from a hybrid dynamical system with their specific dynamics normally unknown. The hybrid nature of such a dynamical system is a result of complex external impacts, which can be summarized as high-frequency and low-frequency from the temporal view, or global and local if we take the spatial view. These impacts also determine the forthcoming development of MTS making them paramount to capture in a time series forecasting task. However, conventional methods face intrinsic difficulties in disentangling the components yielded by each kind of impact from the raw data. To this end, we propose two kinds of normalization modules - temporal and spatial normalization - which separately refine the high-frequency component and the local component underlying the raw data. Moreover, both modules can be readily integrated into canonical deep learning architectures such as Wavenet and Transformer. Extensive experiments on three datasets are conducted to illustrate that, with additional normalization modules, the performance of the canonical architectures can be enhanced by a large margin in the application of MTS and achieves state-of-the-art results compared with existing MTS models.