The GARCH-FuzzyDensity method for density forecasting

This paper introduces a new class of GARCH method, termed the GARCH-Fuzzy-Density method for density forecasting the realizations of a process in which the higher-order moments may be time-varying. The method is based on a probabilistic Takagi-Sugeno fuzzy system and GARCH model.Traditional GARCH models usually assume that the shape of the conditional distribution of a process is conditional only on the first two moments. However, it is well documented that in empirical applications the conditional distribution beyond the first two moments may be conditional on higher-order moments such as skewness. Therefore, traditional GARCH models are insufficient for capturing all aspects of such processes.To resolve the problem mentioned above, the GARCH-FuzzyDensity model was developed. The method is capable of modeling conditional distributions in which the higher-order moments may be time-varying. Therefore, the GARCH-FuzzyDensity model provides more accurate density forecasts for the higher-order moment varying processes than the traditional GARCH models.