On mixture memory GARCH models

We propose a new volatility model, which is called the mixture memory generalized autoregressive conditional heteroskedasticity (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 fractionally integrated GARCH. 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 expectation–maximization 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. Copyright © 2013 Wiley Publishing Ltd.