Empirical Study on Multifractal Properties of Stock Markets

Stock markets take important roles in the world economy. To understand their structures and properties is not only important for market modeling but also helpful for risk management. This paper applies multifractal detrending moving average algorithm (MFDMA) to analyze the multifractal properties of ten stock markets. Generalized Hurst exponent, multifractal scaling exponent and spectrum are computed for each market. The results display that all of these ten markets have non-constant generalized Hurst exponents. Their multifractal scaling exponent curves are not linear. It indicates all of them have multifractal properties. Fat-tailed distribution and long range correlation are important sources of multifractality. In order to analyze their influence on different markets, shuffled data and surrogate data are applied. Shuffling eliminates long range correlation. And surrogate data preserves the correlation and excludes fat-tailed distribution. The results show that fat-tailed distribution has stronger effect for DJI, FCHI, GDAXI, N225, IBOVESPA, JKSE, MXX, SENSEX and SSE indexes. And long correlation possesses stronger influence for FTSE index.