Long-term prediction of time series using fuzzy cognitive maps

摘要

As a powerful recognized knowledge modeling tool, fuzzy cognitive maps (FCMs) have been investigated for time series modeling and forecasting problems. This methodology performs well in one-step-ahead or short-term prediction but poorly in terms of long-term prediction because of the potentially complex interaction between different ensuing steps. In this article, a sound conceptual method is proposed for long-term time series prediction with FCMs, which melds FCMs, time series segmentation and fuzzy clustering. A time series is divided into suitable and internally homogeneous segments. Dynamic time warping is introduced to evaluate the distance between segments. Subsequently, modified fuzzy c-means based on dynamic time warping is utilized to fuzzify these segments such that the segments are transformed into fuzzy time series and semantic vectors. The convex optimization based method is utilized with intent to rapidly and robustly learn FCMs. Consequently, the weight of FCMs can be obtained on the basis of the fuzzy time series. Eventually, the forecasting time segment will be capable of inference according to the formed FCMs and the semantic vectors. In addition, the semantic vectors can intuitively reflect the main characteristics and change tendencies of the time series. To demonstrate the long-term prediction ability of our method, we test it on both synthetic and real-life datasets in comparison with other representative and up-to-date forecasting methods; the superior performance of our method exhibits its excellent capability in forecasting future values.