A Novel Trend-Pattern Unlimited Fuzzy Information Granule-Based Long-Term Forecasting Model for Multivariate Time Series

Long-term forecasting of multivariate time series (MTS) is a crucial yet challenging task due to the intricate interdependencies among variables and the error accumulation over long-term timesteps. Facing with this challenging task, trend fuzzy information granulation has been recognized as an effective approach achieving substantial research outcomes. By transforming numerical time series into granular time series, it captures the trend information in data and effectively alleviates the error accumulation in long-term forecasting. However, existing trend fuzzy information granulation methods typically assume that the trend variations conform to predefined patterns, which limits their ability to accurately model the nonlinear trends presented in real-world MTS data. To overcome this limitation, this paper proposes a trend-pattern unlimited fuzzy information granulation (TUFIG) method for MTS. Unlike traditional methods, TUFIG can adaptively learn trend representations from data without prior assumptions of trend morphology, thereby modeling the nonlinear trends more flexibly. In order to capture the temporal and spatial correlations in the multivariate granular time series transformed from the original time series, we further design a two-stage attention mechanism (TAM). Based on the proposed granulation method and TAM, we develop a long-term forecasting model for MTS. Experimental results on multiple benchmark datasets show that the proposed forecasting model significantly outperforms existing mainstream methods in forecasting accuracy, showcasing substantial application potential. This research not only provides an innovative solution for multivariate time series forecasting but also offers theoretical support for enhancing forecasting accuracy in practical applications.