Time-Series Forecasting Based on High-Order Fuzzy Cognitive Maps and Wavelet Transform

Fuzzy cognitive maps (FCMs) have been successfully used to model and predict stationary time series. However, it still remains challenging to deal with large-scale nonstationary time series, which have trend and vary rapidly with time. In this paper, we propose a time-series prediction model based on the hybrid combination of high-order FCMs (HFCMs) with the redundant wavelet transform to handle large-scale nonstationary time series. The model is termed as Wavelet-HFCM. The redundant Haar wavelet transform is applied to decompose original nonstationary time series into multivariate time series; then, the HFCM is used to model and predict multivariate time series. In learning HFCMs to represent large-scale multivariate time series, a fast HFCM learning method is designed on the basis of ridge regression to reduce the learning time. Finally, summing multivariate time series up yields the predicted time series at each time step. Compared with existing classical methods, the experimental results on eight benchmark datasets show the effectiveness of our proposal, indicating that our prediction model can be applied to various prediction tasks.