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.