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Long-term Prediction of Time Series Based on Fuzzy Cognitive Map And Ensemble Learning

Fuzzy cognitive maps (FCM) have been used as a recognized and powerful knowledge modelling tool for time series modelling and forecasting. The method performs well in single-step forecasting or short-term forecasting, but does not perform well in the field of long-term forecasting due to the complex interrelationships that may exist between the different subsequent steps. This paper proposes an FCM-based long-term time series forecasting model that combines time series granulation, fuzzy C-mean clustering, ensemble learning, and FCM. Firstly, time series are granulated into suitable segments and are isometric, and then these isometric segments are transformed into fuzzy time series and clustering centres using fuzzy C-mean clustering. The BAFCM model is built by combining the Bagging method of ensemble learning and FCM. Subseries of the fuzzy time series are selected randomly using Bootstrap, and then a separate FCM-based learner is used for each subsequence, and each FCM-based learner is learned quickly and robustly based on a convex optimisation method. The output of multiple base learners is then combined using a weighted average method to obtain the predicted output of the fuzzy time series, which is finally extrapolated together with the clustering centres to achieve long-term prediction of the time series. To demonstrate the performance of our method in long-term prediction, we tested it on synthetic and real-life time series and compared it with other representative prediction methods. The experiments demonstrate the superiority of our method in the long-term prediction of time series.