A HYBRID WAVELET-HIGH ORDER FUZZY COGNITIVE MAPS AND RANDOM FOREST REGRESSION APPROACH FOR TIME SERIES FORECASTING
Abstract
Time series forecasting becomes more critical, especially when linear, non-stationary and uncertain data are available. This paper proposes an innovative hybrid model that combines wavelet transforms, high-order fuzzy cognitive maps and random forest regression for high-accuracy prediction of time series. This hybrid approach aims to overcome the limitations of traditional time series analysis methods. In the approach, wavelet coefficients are enhanced by the integration of higher-order fuzzy cognitive maps, which allows for efficient modeling of nonlinear relationships through quadratic interactions. Four different wavelet transforms (Morlet, Mexican Hat, Haar, Daubechies) are used in the model and these structures are systematically compared. The model is trained with a Random Forest Regression model and hyperparameter optimization was performed using GridSearchCV. Model performance is evaluated on data sets of atmospheric CO2 concentrations, El Niño Sea surface temperatures and sunspot activity records from Mauna Loa Observatory. A comprehensive analysis is presented by evaluating the model performances with multiple metrics such as symmetric mean absolute percentage error, root mean squared error, mean absolute percentage error, and mean absolute scaled error. The experimental results show that the Mexican Hat wavelet performs the best in all data sets. It outperformed the other methods with root mean square error values of 0.2414 on CO2 data, 0.1621 root mean square error on El Niño temperature prediction and 4.3279 root mean square error on sunspot activity. While continuous wavelets are more successful than discrete wavelets, the integration of hybrid structure significantly improves the model's ability to capture nonlinear relationships. This research not only proves the superiority of wavelet-based hybrid models in time series analysis, but also demonstrates the potential for practical application in areas such as climate, meteorology, and space weather studies.
Keywords
Time series prediction, Wavelet, Transform, Fuzzy cognitive maps, Hybrid model, Random forest
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