We propose a new volatility model, which is called the mixture memory GARCH (MM-GARCH) model. The MM-GARCH model has two mixture components, of which one is a short memory GARCH and the other is the long memory FIGARCH. The new model, a special ARCH(∞) process with random coefficients, possesses both the properties of long memory volatility and covariance stationarity. The existence of its stationary solution is discussed. A dynamic mixture of the proposed model is also introduced. Other issues, such as the EM algorithm as a parameter estimation procedure, the observed information matrix which is relevant in calculating the theoretical standard errors, and a model selection criterion are also investigated. Monte Carlo experiments demonstrate our theoretical findings. Empirical application of the MM-GARCH model to the daily S&P 500 index illustrates its capabilities.
Keywords: long memory in volatility, covariance stationarity, mixture ARCH(∞), EM algorithm.