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This paper proposes an innovative  semiparametric nonlinear fuzzy-EGARCH-ANN  model to solve the problem of accurate modeling for forecasting stock market volatility. This model has been developed by a combination of the FIS, ANN, and EGARCH models. Because the proposed model is highly nonlinear and gradient-based parameter estimation methods might not give global optimal parameters for highly nonlinear models, the study has decided to use evolutionary algorithms instead. In particular, a differential evolution (DE) algorithm is suggested to solve the parameter estimation problem of the proposed model. After this, the semiparametric nonlinear fuzzy-EGARCH-ANN model has been developed mathematically from the three models mentioned before, and the study has simulated data by it. After the simulation, parameter estimation of the proposed model using a differential evolution algorithm on the simulated data is done. Finally, it is seen that the proposed model is good in capturing the volatility clustering and leverage effects of highly nonlinear and complicated financial time series data that were overlooked by the EGARCH model.

Improving Forecasts of the EGARCH Model Using Artificial Neural Network and Fuzzy Inference System