Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis

We divided the whole series of Shenzhen stock market into two sub-series at the criterion of the date of a reform and their scale behaviors are investigated using multifractal detrended fluctuation analysis (MF-DFA). Employing the method of rolling window, we find that Shenzhen stock market was becoming more and more efficient by analyzing the change of Hurst exponent and a new efficient measure, which is equal to multifractality degree sometimes. We also study the change of Hurst exponent and multifractality degree of volatility series. The results show that the volatility series still have significantly long-range dependence and multifractality indicating that some conventional models such as GARCH and EGARCH cannot be used to forecast the volatilities of Shenzhen stock market. At last, the abnormal phenomenon of multifractality degrees for return series is discussed. The results have very important implications for analyzing the influence of policies, especially under the environment of financial crisis.