Forecasting volatility of stock market using adaptive Fuzzy-GARCH model

In this paper, we study the problem of volatility forecasting of financial stock market. In general, stock market volatility is time-varying and nonlinear, and exhibits properties of clustering. This paper shows results from using the method of fuzzy systems to analyze the nonlinear in the case of generalized autoregressive conditional heteroskedasticity (GARCH) models and using the adaptive method of recursive least-squares (RLS) to forecast the stock market volatility. The joint the parameters of membership functions and GARCH model is a rather high nonlinear and complicated problem. This study presents an iterative algorithm based on genetic ones to estimate parameters of the membership functions and GARCH model. The genetic algorithm (GA) method aims to achieve a global optimal solution with a fast convergence rate for this Fuzzy-GARCH model estimation problem. From the simulation results, we have determined that the both estimation of in-sample and forecasting of out-of-sample volatility performance are significantly improved, if the both of leverage effect and adaptive forecast are considered in the GARCH model.