Different from many previous studies which only applied one approach to analyze the multifractal properties of the stock market, this manuscript applies the partition function method (PF) and the multifractal detrended fluctuation analysis (MF-DFA) to investigate the multifractal properties of index distribution and fluctuations of the main stock markets in the world. After comparing the differences between the two multifractal approaches, it is found that the price distribution characteristic can be discovered by the partition function method, while the price fluctuation characteristic can be revealed via the MF-DFA. The empirical results show that index distribution and fluctuation multifractal properties of one stock market are different, so we can investigate the difference among the stock markets more comprehensively by applying the two approaches simultaneously.
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