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.

中文翻译：

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基于高阶模糊认知图和小波变换的时间序列预测

模糊认知图 (FCM) 已成功用于建模和预测平稳时间序列。然而，处理具有趋势且随时间快速变化的大规模非平稳时间序列仍然具有挑战性。在本文中，我们提出了一种基于高阶 FCM (HFCM) 与冗余小波变换的混合组合的时间序列预测模型，以处理大规模非平稳时间序列。该模型被称为小波-HFCM。应用冗余Haar小波变换将原始非平稳时间序列分解为多元时间序列；然后，HFCM 用于建模和预测多元时间序列。在学习 HFCM 表示大规模多元时间序列时，在岭回归的基础上设计了一种快速 HFCM 学习方法，以减少学习时间。最后，将多元时间序列相加会在每个时间步产生预测的时间序列。与现有的经典方法相比，在八个基准数据集上的实验结果表明了我们的建议的有效性，表明我们的预测模型可以应用于各种预测任务。