Applying a combined fuzzy systems and GARCH model to adaptively forecast stock market volatility

This paper studies volatility forecasting in the financial stock market. In general, stock market volatility is time-varying and exhibits clustering properties. Thus, this paper presents the results of using a fuzzy system method to analyze clustering in generalized autoregressive conditional heteroskedasticity (GARCH) models. It also uses the adaptive method of recursive least-squares (RLS) to forecast stock market volatility.The fuzzy GARCH model represents a joint estimation method; the membership function parameters together with the GARCH model parameters make this problem of stock market is highly nonlinear and complicated. This study presents an iterative algorithm based on a genetic algorithm (GA) to estimate the parameters of the membership functions and the GARCH models. In this paper, the GA method is employed to identify a global optimal solution with a fast convergence rate in the context of the fuzzy GARCH model estimation problem studied here. Based on simulation results, we determined that both the estimation of in-sample and the forecasting of out-of-sample volatility performance are significantly improved when the GARCH model considers both the clustering effect and the adaptive forecast.