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.

In this paper, a robust analysis of volatility forecasting of the GBP-ETB exchange rate was provided using weekly data spanning the period June 30, 2003-January 24, 2020. To our knowledge, this was the first study that focuses on the GBP-ETB exchange rate using high-frequency data and the Fuzzy-EGARCH-ANN econometric model. The research finds that the best performing model in terms of one-step ahead forecasts based on realized volatility computed from the underlying daily data series is the Fuzzy-EGARCH-ANN(1, 2, 2, 1) with students t-distribution.

This work shown as the fuzzy-EGARCH-ANN (fuzzy-exponential generalized autoregressive conditional heteroscedastic-artificial neural network) model does not require continuous model calibration if the corresponding DE algorithm is used appropriately, but other models such as GARCH, EGARCH, and EGARCH-ANN need continuous model calibration and validation so they fit the data and reality very well up to the desired accuracy. Also, a robust analysis of volatility forecasting of the daily S&P 500 data collected from Yahoo Finance for the daily spanning period 1/3/2006 to 20/2/2020. To our knowledge, this is the first study that focuses on the daily S&P 500 data using high-frequency data and the fuzzy-EGARCH-ANN econometric model. Finally, the research finds that the best performing model in terms of one-step-ahead forecasts based on realized volatility computed from the underlying daily data series is the fuzzy-EGARCH-ANN (1,1,2,1) model with Student’s t-distribution.