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Detrended fluctuation analysis (DFA), detrended cross-correlation fluctuation analysis (DCCA) and multifractal methods are applied to the time-scaling properties analysis of daily closing prices of Shanghai composite index (SHCI) and Shenzhen composite index (SZCI) of Chinese stock market. The results show that these index series are characterised by long-term memory, multifractal scaling and power-law behavior, and these characteristics have obvious differences between the SHCI and SZCI. The comparison results suggest that heterogeneity (disordered state) characterises of the SHCI dynamics owing to the wider fluctuation of the power of impulsion and suppression outside to stock, and other related factors in Shanghai stock market than that of SZCI in Shenzhen stock market. Furthermore, we investigated the frequency-size distribution of SHCI and SZCI series. This work can be helpful to improvement of modelling of Chinese stock market.

The Time-Scaling Analysis of Chinese Stock Market Based on Fractal Methods