A two-stage model for time series prediction based on fuzzy cognitive maps and neural networks

This paper proposes a two-stage prediction model, for multivariate time series prediction based on the efficient capabilities of evolutionary fuzzy cognitive maps (FCMs) enhanced by structure optimization algorithms and artificial neural networks (ANNs). In the first-stage, an evolutionary FCM is constructed automatically from historical time series data using the previously proposed structure optimization genetic algorithm, while in the second stage, the produced FCM defines the inputs in an ANN which next is trained by the back propagation method with momentum and Levenberg-Marquardt algorithm on the basis of available data. The structure optimization genetic algorithm for automatic construction of FCM is implemented for modeling complexity based on historical time series data, selecting the most important nodes (attributes) and interconnections among them thus providing a less complex and efficient FCM-based model. This model is used next as input in an ANN. ANNs are used at the final process for making time series prediction considering as inputs the concepts defined by the produced FCM. The previously proposed structure optimization genetic algorithm for FCM construction by historical data as well as the ANN have been already proved their efficacy on time series forecasting. The performance of the proposed approach is presented through the analysis of multivariate historical data of benchmark datasets for making predictions. The multivariate analysis of historical data is held for a large number of input variables, like season, month, day or week, holiday, mean and high temperature, etc. The whole approach was implemented in an intelligent software tool initially deployed for FCM prediction. Through the experimental analysis, the usefulness of the new two-stage approach in time series prediction is demonstrated, by calculating seven prediction performance indicators which are well known from the literature.