Abstract
This paper introduces an adaptive fuzzy rule-based system applied as a financial time series model for volatility forecasting. The model is based on Takagi–Sugeno fuzzy systems and is built in two phases: In the first, the model uses the subtractive clustering algorithm to determine initial group structures in a reduced data set. In the second phase, the system is modified dynamically by adding and pruning operators and applying a recursive learning algorithm based on the expectation maximization optimization technique. The algorithm automatically determines the number of fuzzy rules necessary at each step, and one-step-ahead predictions are estimated and parameters updated. The model is applied to forecast financial time series volatility, considering daily values of the São Paulo stock exchange index, the Petrobras preferred stock prices, and the BRL/USD exchange rate. The model suggested is compared against generalized autoregressive conditional heteroskedasticity models. Experimental results show the adequacy of the adaptive fuzzy approach for volatility forecasting purposes.