The modeling and prediction of time series based on synergy of high-order fuzzy cognitive map and fuzzy c-means clustering

摘要

The time series prediction models based on fuzzy set theory have been widely applied to diverse fields such as enrollments, stocks, weather and etc., as they can handle prediction problem under uncertain circumstances in which data are incomplete or vague. Researchers have presented diverse approaches to support the development of fuzzy time series prediction models. While the existing approaches exhibit two evident shortcomings: one is that they have low efficiency of development, which is hardly applicable in the prediction problem involving large-scale time series, and the other is that fuzzy logical relationships mined in an ad hoc way cannot uncover the global characteristics of time series, which reduces accuracy of the resulting model. In this paper, a novel modeling and prediction approach of time series based on synergy of high-order fuzzy cognitive map (HFCM) and fuzzy c-means clustering is proposed, in which fuzzy c-means clustering algorithm is used to construct information granules, transform original time series into granular time series and generate a structure of HFCM prediction model in an automatic fashion. Subsequently depending on historical data of time series, the HFCM prediction model of time series is completely formed by exploiting PSO algorithm to learn all parameters of one. Finally, the developed HFCM prediction model can realize numeric prediction by performing inference in the granular space. Four benchmark time series data sets with different statistical characteristics coming from different areas are applied to validate the feasibility and effectiveness of the proposed modeling approach. The obtained results clearly show the effectiveness of the approach. The developed HFCM prediction models depend on historical data of time series and is emerged in the form of map, which is simpler, legible and have high-level interpretability. Additionally, the proposed approach also exhibits a clear ability to handle the prediction problem of large-scale time series.