Adaptive Fuzzy-GARCH model applied to forecasting the volatility of stock markets using particle swarm optimization

Fluctuations in the stock market follow the principle of volatility clustering in which changes are cataloged by similarity; as such, large changes tend to follow large changes, and small changes tend to follow small changes. This clustering is one of the major reasons why many generalized autoregression conditional heteroscedasticity (GARCH) models do not forecast the stock market well. In this paper, an adaptive Fuzzy-GARCH model with particle swarm optimization (PSO) is proposed to solve this problem. The adaptive Fuzzy-GARCH model refers to both GARCH models and the parameters of membership functions, which are determined by the characteristics of market itself. Here, we present an iterative algorithm based on PSO to estimate the parameters of the membership functions. The PSO method aims to achieve a global optimal solution with a rapid convergence rate. The three stock markets of Taiwan, Japan, and Germany were analyzed to illustrate the performance of the proposed method.