High and low or close to close prices? Evidence from the multifractal volatility

• We examine the daily returns and range returns when forecasting multifractal volatility.
• Both of the two series present the persistence and exhibit the multifractal features.
• There exists the well-established phenomenon of “leverage effects”.
• Daily returns have a greater power than the range returns in forecasting.

In this study, we examine the daily returns and daily range returns dependent on close–close and the high–low prices when forecasting multifractal volatility in the Chinese stock market. In in-sample forecasting we find that both the daily returns and range returns have a significant impact on the future multifractal volatility, existing the well-established phenomenon of “leverage effects” of the positive and negative returns. Moreover, using the MF-DFA method, we find that both the two series present the persistence and exhibit the multifractal features. Furthermore, our MCS test results show that the ARFIMA-lnMFV-R and ARFIMA-lnMFV-LR models provide relatively superior volatility forecasts in comparison to all other models. Finally, we find that the daily returns calculated by close to close prices have a greater power than the daily range return calculated by high and low prices in forecasting.