Modeling and forecasting carbon dioxide emission allowance spot price volatility : multifractal vs. GARCH-type volatility models

This paper applies Markov-switching multifractal (MSM) processes to model and forecast carbon dioxide (CO2) emission price volatility, and compares their forecasting performance to the standard GARCH, fractionally integrated GARCH (FIGARCH) and the two-state Markov-switching GARCH (MS-GARCH) models via three loss functions (the mean squared error, the mean absolute error and the value-at-risk). We evaluate the performance of these models via the superior predictive ability test. We find that the forecasts based on the MSM model cannot be outperformed by its competitors under the vast majority of criteria and forecast horizons, while MS-GARCH mostly comes out as the least successful model. Applying various VaR backtesting procedures, we do, however, not find significant differences in the performance of the candidate models under this particular criterion. We also find that we cannot reject the null hypothesis of MSM forecasts encompassing those of GARCH-type models. In line with this result, optimally combined forecasts do indeed hardly improve upon the best single models in our sample.