Using empirical wavelet transform and high-order fuzzy cognitive maps for time series forecasting

Abstract

Many studies on time series forecasting have employed fuzzy cognitive maps (FCMs). However, it is required to develop techniques capable of effective responses and great accuracy for large-scale non-stationary time series, such as sharp-fluctuated datasets. For forecasting such data, the present study introduces an accurate, precise, and efficient combined forecasting framework with ridge regression, high-order FCM (HFCM), and empirical wavelet transform (EWT). The proposed learning method named as EWTHFCM. This model employs EWT for non-stationary time series transformation into a multivariate sequence. The HFCM then models each multivariate time series through a node. For the optimized learning part, ridge regression is employed to perform the process for the HFCM representation of large-scale time series. The main reasons to choose the ridge regression are its circle-like phenomenon which makes it a perfect fit for being combined with EWT. This fitness is due to the optimal filter bank selection behavior and adaptivity feature of EWT, eventually making the ridge regression fast, efficient, and accurate. Subsequently, HFCM models and forecasts the multivariate time series and helps find the trend pattern. Then, the multivariate time series is reconstructed by inverse EWT to predict time series at all time steps. The root mean square error (RMSE) is measured on 15 real-life standard datasets, of which 8 are utilized to compare the proposed framework to 11 state-of-art algorithms. According to the experimental results and comparison with other research papers, we recommend using EWTHFCM as a new, superior, and accurate method for many forecasting purposes and circumstances.