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

Abstract

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.

Model Calibration and Validation for the Fuzzy-EGARCH-ANN Model

“…As proposed by the authors, the fuzzy-EGARCH-ANN model is described by a collection of fuzzy rules in the form of If-en statements in order to describe the stock fluctuations with volatility clustering overlooked by EGARCH-ANN model via fuzzy rules and the asymmetric responses of volatility to positive and negative shocks via an EGARCH-ANN model [18].…”

Modeling Exchange Rate Volatility Dynamics of the Great Britain Pound to Ethiopian Birr Using the Semi-Parametric Non-Linear Fuzzy-EGARCH-ANN Model

“…The Fuzzy-EGARCH-ANN model is described by a collection of fuzzy rules in the form of If-Then statements in order to describe the stock fluctuations with volatility clustering overlooked by EGARCH-ANN model via Fuzzy rules and the asymmetric responses of volatility to positive and negative shocks via an EGARCH-ANN model [11].…”

“…The output of this Fuzzy-EGARCH-ANN model is the weighted average of each individual rule and is obtained by using FIS fundamental steps as in [11] and [12] as follows:…”

“…A local model contributes to the overall output which is proportional to the normalized degree of the firing of each rule. As a result, the exponential of this weighted average value gives us the predicted stock market return volatility using our newly proposed model [11].…”

“…The design of the Fuzzy-EGARCH-ANN model includes the determination of the unknown parameters, namely the parameters of the consequent parts of the fuzzy If-Then rules by minimizing the prediction error [11]. Therefore, to estimate the Fuzzy-EGARCH-ANN model parameters without suffering from local optimum, Differential Evolution (DE) algorithm with Archive is used [11]. Furthermore, step by step self-explanatory summary of the algorithm that we have used in this study is given by Table 1.…”