Title: Modelling volatility cycles: The $(MF)^2$ GARCH model
Authors: Christian Conrad - Heidelberg University (Germany) [presenting]
Robert Engle - NYU Stern (United States)
Abstract: A multiplicative factor multi-frequency ($(MF)^2$) component GARCH model is proposed. The model consists of a short-term GARCH component and one or multiple long-term components. The long-term components are based on MEM equations for the average standardized forecast errors of the GARCH component and capture the counter-cyclical behavior of financial volatility. We derive conditions weak stationarity of the $(MF)^2$ GARCH and discuss the news impact function. Since the new model is dynamically complete, it is straightforward to construct multi-step ahead volatility forecasts. We apply the model to forecast the volatility of the S\&P 500 and three international stock markets. We show that the long-term component of the S\&P 500 behaves counter-cyclical and is driven by news about the macroeconomic outlook. The $(MF)^2$ GARCH significantly outperforms the nested one-component GJR GARCH in out-of-sample forecasting.