Multiscale adaptive multifractal analysis and its applications.

To precisely analyze the fractal nature of a short-term time series under the multiscale framework, this study introduces multiscale adaptive multifractal analysis (MAMFA) combining the adaptive fractal analysis method with the multiscale multifractal analysis (MMA). MAMFA and MMA are both applied to the two kinds of simulation sequences, and the results show that the MAMFA method achieves better performances than MMA. MAMFA is also applied to the Chinese and American stock indexes and the R-R interval of heart rate data. It is found that the multifractal characteristics of stock sequences are related to the selection of the scale range s. There is a big difference in the Hurst surface's shape of Chinese and American stock indexes and Chinese stock indexes have more obvious multifractal characteristics. For the R-R interval sequence, we find that the subjects with abnormal heart rate have significant shape changes in three areas of Hurst surface compared with healthy subjects, thereby patients can be effectively distinguished from healthy subjects.