An evolutionary hybrid Fuzzy Computationally Efficient EGARCH model for volatility prediction

•A hybrid Fuzzy-FLANN EGARCH model is proposed to forecast the volatility of three stock market indexes.•The TSK-type fuzzy inference system uses FLANN in the consequent part of the fuzzy rules for improved mapping.•The leverage effect, asymmetric shock by leverage effect of EGARCH model are important for forecasting.•A differential evolution based learning strategy is used for EGARCH-FLANN model parameters.•Multistep prediction and statistical tests are also included.

Accurate modeling for forecasting of stock market volatility is a widely interesting research area both in academia as well as financial markets. This paper proposes an innovative Fuzzy Computationally Efficient EGARCH model to forecast the volatility of three stock market indexes. The proposed model represents a joint estimation of the membership function parameters of a TSK-type fuzzy inference system along with the leverage effect, asymmetric shock by leverage effect of EGARCH model in forecasting highly nonlinear and complicated financial time series model more accurately. Further unlike the conventional TSK type fuzzy neural network the proposed model uses a functional link neural network (FLANN) in the consequent part of the fuzzy rules to provide an improved mapping. Moreover, a differential evolution (DE) algorithm is suggested to solve the parameters estimation problem of Fuzzy Computationally Efficient EGARCH model. Being a parallel direct search algorithm, DE has the strength of finding global optimal solutions regardless of the initial values of its few control parameters. Furthermore, the DE based algorithm aims to achieve an optimal solution with a rapid convergence rate. The proposed model has been compared with some GARCH family models and hybrid fuzzy systems and GARCH models based on three performance metrics: MSFE, RMSFE, and MAFE. The results indicate that the proposed method offers significant improvements in volatility forecasting performance in comparison with all other specified models.

Graphical abstractFramework of the proposed Fuzzy CE-EGARCH modelFigure optionsDownload full-size imageDownload as PowerPoint slide