Double Decomposition and Fuzzy Cognitive Graph-Based Prediction of Non-Stationary Time Series

Abstract

Deep learning models, such as recurrent neural network (RNN) models, are suitable for modeling and forecasting non-stationary time series but are not interpretable. A prediction model with interpretability and high accuracy can improve decision makers’ trust in the model and provide a basis for decision making. This paper proposes a double decomposition strategy based on wavelet decomposition (WD) and empirical mode decomposition (EMD). We construct a prediction model of high-order fuzzy cognitive maps (HFCM), called the WE-HFCM model, which considers interpretability and strong reasoning ability. Specifically, we use the WD and EDM algorithms to decompose the time sequence signal and realize the depth extraction of the signal’s high-frequency, low-frequency, time-domain, and frequency domain features. Then, the ridge regression algorithm is used to learn the HFCM weight vector to achieve modeling prediction. Finally, we apply the proposed WE-HFCM model to stationary and non-stationary datasets in simulation experiments. We compare the predicted results with the autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) models.For stationary time series, the prediction accuracy of the WE-HFCM model is about 45% higher than that of the ARIMA, about 35% higher than that of the SARIMA model, and about 16% higher than that of the LSTM model. For non-stationary time series, the prediction accuracy of the WE-HFCM model is 69% higher than that of the ARIMA and SARIMA models.

Keywords

• non-stationary time series prediction
• high-order cognitive fuzzy map
• wavelet decomposition
• empirical mode decomposition
• ridge regression