Evolving Fuzzy-GARCH Approach for Financial Volatility Modeling and Forecasting

Volatility modeling and forecasting play a key role in asset allocation, risk management, derivatives pricing and policy making. The purpose of this paper is to develop an evolving fuzzy-GARCH modeling approach for stock market asset returns forecasting. The method addresses GARCH volatility modeling within the framwork of evolving fuzzy systems. This hybrid methodology aims to account for time-varying volatility, from GARCH approach, as well as volatility clustering and nonlinear time series identification, from evolving fuzzy systems, which use time-varying data streams to continuously and simultaneously adapt the structure and functionality of fuzzy models. The motivation is to improve model performance as new data is input through gradual model construction, inducing model adaptation and refinement without catastrophic forgetting while keeping current model useful. An empirical application includes the forecasting of S&P 500 and Ibovespa indexes by the evolving fuzzy-GARCH against traditional GARCH-family models and a fuzzy GJR-GARCH methodology. The results indicate the high potential of the evolving fuzzy-GARCH model to forecast stock returns volatility, which outperforms GARCH-type models and showed comparable forecasts with fuzzy GJR-GARCH methodology.