Which is the better forecasting model? A comparison between HAR-RV and multifractality volatility

In this paper, by taking the 5-min high frequency data of the Shanghai Composite Index as example, we compare the forecasting performance of HAR-RV and Multifractal volatility, Realized volatility, Realized Bipower Variation and their corresponding short memory model with rolling windows forecasting method and the Model Confidence Set which is proved superior to SPA test. The empirical results show that, for six loss functions, HAR-RV outperforms other models. Moreover, to make the conclusions more precise and robust, we use the MCS test to compare the performance of their logarithms form models, and find that the HAR-log(RV) has a better performance in predicting future volatility. Furthermore, by comparing the two models of HAR-RV and HAR-log(RV), we conclude that, in terms of performance forecasting, the HAR-log(RV) model is the best model among models we have discussed in this paper.