Multifractal Analysis of Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index

We have performed a detailed multifractal analysis on the Shanghai Stock Exchange Composite Index (SHSECI) and Shenzhen Stock Exchange Component Index (SZSECI). The partition function χ_q(e), generalized fractal dimensions D_q, singularity α and multifractal spectrum f(α) are calculated. It is found that the partition function χ_q(e) scales as a power law with respect to the box size e and both series obey multifractal scaling, rather then being a simple monofractal. Furthermore, the Δf=f(α_min)−f(α_max) of both series is less than zero and the range of singularity α of SHSECI is narrower than that of SZSECI, which indicated that the ratio of number of highest index moments is less than that of lowest ones and the variation of SHSECI is smaller than that of SZSECI.