  By adopting Multifractal detrended fluctuation (MF-DFA) analysis methods, the
multifractal nature is revealed in the high-frequency data of two typical
indexes, the Shanghai Stock Exchange Composite 180 Index (SH180) and the
Shenzhen Stock Exchange Composite Index (SZCI). The characteristics of the
corresponding multifractal spectra are defined as a measurement of market
volatility. It is found that there is a statistically significant relationship
between the stock index returns and the spectral characteristics, which can be
applied to forecast the future market return. The in-sample and out-of-sample
tests on the return predictability of multifractal characteristics indicate the
spectral width $\Delta {\alpha}$ is a significant and positive excess return
predictor. Our results shed new lights on the application of multifractal
nature in asset pricing.
