A Long- Term Forecasting Method for Time Series based on Multi-Scale Fuzzy Information Granulation using Double-Layer Fuzzy Cognitive Maps

Univariate time series, as a simple form of data, have been extensively studied in various fields. However, due to their limited information and high complexity, related issues are challenging. Long-term forecasting for such data is particularly difficult due to the cumulative error effect, which causes most methods to perform poorly. This paper, leveraging the innate advantage of information fuzzy granules in predicting long-term trends, proposes a long-term forecasting method based on multi-scale fuzzy information granules(MSFIG) and double-layer fuzzy cognitive maps(DLFCM) to address this issue. The method is divided into two parts: data representation and data prediction. The data representation section introduces MSFIGs, which effectively expand the information of univariate time series data and solve the problem of selecting segmentation sizes during the time series granulation process. Two types of related information particles are constructed using equal-spacing and unequal-spacing segmentation methods, thereby better representing data characteristics and balancing temporal interpretability and local information features. To maximize the utilization of this time series particle structure, the fuzzy cognitive map was improved. A two-layer FCMs nested structure was used to model the causal relationships of the two types of particle information, learning their global and local trend information, thus achieving long-term forecasting for univariate time series. This paper compares the proposed method with various long-term forecasting methods on two public datasets, verifying the effectiveness of the proposed method.