TVC Former: A transformer-based long-term multivariate time series forecasting method using time-variable coupling correlation graph

Abstract

Long-term multivariate time series forecasting is crucial in various domains that require the effective modeling of intervariable dependencies in series data. However, existing methods tend to capture these dependencies directly across the entire series, thus neglecting the local dynamic characteristics of the intervariable correlation patterns caused by locality differences and the dynamic variability of the series. To address this, we propose TVC Former, a forecasting model that uses a time-variable coupling correlation graph (TVC graph). The TVC graph treats local window-level subsequences as nodes and explicitly models local intervariable dependence. Its structure is dynamically and adaptively generated to effectively represent task-specific valuable intervariable local correlation patterns while eliminating irrelevant ones. Specifically, a sparsified graph structure is initialized based on the correlation between the input historical series and statistical similarity between the subsequences. It is then optimized using a pattern capture-fusion sparsification unit with learnable parameters. In addition, we propose a time-variable joint-encoding framework with a transformer encoder as the backbone. By introducing local head markers and a graph neural network, the framework effectively captures the intervariable dependencies using the TVC graph. Experiments on seven real-world datasets demonstrate the superiority of TVC Former in long-term forecasting tasks.