A fuzzy GARCH model applied to stock market scenario using a genetic algorithm

In this paper, we derive a new application of fuzzy systems designed for a generalized autoregression conditional heteroscedasticity (GARCH) model. In general, stock market performance is time-varying and nonlinear, and exhibits properties of clustering. The latter means simply that certain large changes tend to follow other large changes, and in general small changes tend to follow other small changes. This paper shows results from using the method of functional fuzzy systems to analyze the clustering in the case of a GARCH model.The optimal parameters of the fuzzy membership functions and GARCH model are extracted using a genetic algorithm (GA). The 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 performance is significantly improved if the leverage effect of clustering is considered in the GARCH model. The simulations use stock market data from the Taiwan weighted index (Taiwan) and the NASDAQ composite index (NASDAQ) to illustrate the performance of the proposed method.