Time series forecasting based on kernel mapping and high-order fuzzy cognitive maps

Abstract Fuzzy cognitive maps (FCMs) have emerged as a powerful tool for dealing with the task of time series prediction. Most existing research devoted to designing an effective method to extract feature time series from the original time series, which are used to construct FCMs and predict the time series. However, in existing methods, all extracted feature time series, including the redundant feature time series, were used to develop FCMs instead of selecting the key feature time series (KFTS) to construct FCMs, which limits the generalization and prediction accuracy of the models. In this paper, we propose a framework based on kernel mapping and high-order FCMs (HFCM) to forecast time series inspired by the kernel methods and support vector regression (SVR). The model is termed as Kernel-HFCM. Kernel mapping is designed to map the original one-dimensional time series into multidimensional feature time series, and then the feature selection algorithm is proposed to select the KFTS from the multidimensional feature time series to develop the HFCM. Finally, reverse kernel mapping is used to map the feature time series back to the predicted one-dimensional time series. In comparison to the existing methods, the experimental results on seven benchmark datasets demonstrate the effectiveness of Kernel-HFCM in time series prediction.