We propose the EGARCH-MIDAS-CPU model, which incorporates the leverage effect and climate policy uncertainty (CPU) to model and forecast European Union allowance futures’ (EUAF) volatility. An empirical analysis based on the daily data of the EUAF price index and the monthly data of the CPU index using the EGARCH-MIDAS-CPU model shows that the EUAF’s volatility exhibits a leverage effect, and the CPU has a significantly negative impact on the EUAF’s volatility. Furthermore, out-of-sample analysis based on three loss functions and the Model Confidence Set (MCS) test suggests that EGARCH-MIDAS-CPU model yields more accurate out-of-sample volatility forecasting results than various competing models. There is room for further application of the model, such as this model could be applied to price carbon futures, so as to improve the liquidity of the carbon market and achieve carbon peak and carbon neutrality as soon as possible.

There is increasing evidence that European Union allowance (EUA) futures return distributions exhibit features of time-varying higher moments (skewness and kurtosis), which plays an important role in modeling and forecasting EUA futures volatility. Moreover, a number of studies have shown that time-varying risk aversion (RA) contains useful information for forecasting EUA futures volatility. In light of this, this paper proposes the GARCH-MIDAS with skewness and kurtosis (hereafter GARCH-MIDAS-SK) to empirically investigate the impact and predictive role of RA on EUA futures volatility. Our empirical results show that RA has a significantly negative impact on the long-term volatility of EUA futures. The EUA futures return distributions exhibit obvious features of time-varying higher moments. Incorporating RA and time-varying higher moments improves the in-sample fitting of the model. Furthermore, out-of-sample results suggest that incorporating RA and time-varying higher moments leads to significantly more accurate volatility forecasts. This finding is robust to alternative out-of-sample forecasting windows.

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