Forecasting the volatility of European Union allowance futures with macroeconomic variables using the GJR-GARCH-MIDAS model

Abstract

Building on the GJR-GARCH model, this paper uses the mixed-data sampling (MIDAS) approach to link monthly realized volatility of EU carbon future prices and macroeconomic variables to the volatility of EU carbon futures market and proposes the GJR-GARCH-MIDAS model incorporating macroeconomic variables including the economic sentiment indicator of the EU, the harmonized index of consumer prices of the EU, the European economic policy uncertainty index and ECB’s marginal lending facility rate (GJR-GARCH-MIDAS-X models). An empirical analysis based on the monthly macroeconomic variables and daily EUA futures data shows that the above four low-frequency macroeconomic variables have significant positive or negative impacts on the long-term volatility of EUA future prices, respectively. The GJR-GARCH-MIDAS-X models significantly outperform other competing models, including the GJR-GARCH model, GARCH-MIDAS model and standard GJR-GARCH-MIDAS model, in terms of out-of-sample volatility forecasting, which suggests that macroeconomic variables contain important information for EUA future price volatility forecasts. In particular, the GJR-GARCH-MIDAS model with harmonized index of consumer prices (HICP) (GJR-GARCH-MIDAS-HICP model) performs best in out-of-sample volatility forecasting, and our findings are robust to different forecasting windows.