Multi-scale convolution enhanced transformer for multivariate long-term time series forecasting

In data analysis and forecasting, particularly for multivariate long-term time series, challenges persist. The Transformer model in deep learning methods has shown significant potential in time series forecasting. The Transformer model's dot-product attention mechanism, however, due to its quadratic computational complexity, impairs training and forecasting efficiency. In addition, the Transformer architecture has limitations in modeling local features and dealing with multivariate cross-dimensional dependency relationship. In this article, a Multi-Scale Convolution Enhanced Transformer model (MSCformer) is proposed for multivariate longterm time series forecasting. As an alternative to modeling the time series in its entirety, a segmentation strategy is designed to convert the input original series into segmented forms with different lengths, then process time series segments using a new constructed multi-Dependency Aggregation module. This multi- Scale segmentation approach reduces the computational complexity of the attention mechanism part in subsequent models, and for each segment of length corresponds to a specific time scale, it also ensures that each segment retains the semantic information of the data sequence level, thereby comprehensively utilizing the multi-scale information of the data while more accurately capturing the real dependency of the time series. The Multi-Dependence Aggregate module captures both cross-temporal and cross-dimensional dependencies of multivariate long-term time series and compensates for local dependencies within the segments thereby captures local series features comprehensively and addressing the issue of insufficient information utilization. MSCformer synthesizes dependency information extracted from various temporal segments at different scales and reconstructs future series using linear layers. MSCformer exhibits higher forecasting accuracy, outperforming existing methods in multiple domains including energy, transportation, weather, electricity, disease and finance.