Stock market volatility comprises complex characteristics of time-varying irregular behavior and asymmetric clustering properties with respect to both positive and negative stock index returns. In this paper, we present a fuzzy-GARCH model to analyze asymmetric clustering properties and a robust Kalman filter to address the problem of the time-varying irregular behavior of volatility. In our approach, we first use a fuzzy system to analyze clustering regimes based on stock market index returns. Second, we use the clustering regimes of the first stage to set up generalized autoregressive conditional heteroskedasticity (GARCH) models and reformulated state space. Finally, we use a robust Kalman filter to reduce time-varying complexity when forecasting volatility. The proposed method is based on state space and joins the parameters of membership functions and GARCH models that are highly complex and nonlinear. We present an iterative algorithm based on particle swarm optimization to estimate parameters of the membership functions and GARCH models. The effectiveness of the approach is demonstrated on stock market data from the Taiwan Stock Exchange Weighted Index (Taiwan), Hang Seng Index (Hong Kong), and Japan Nikkei 225 Index (Japan). From the simulation results, we determine that forecasting of out-of-sample volatility performance is significantly improved when the GARCH model considers both asymmetric effect and robust adaptive forecasting.
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