Optimal Setting for Hurst Index Estimation and Its Application in Chinese Stock Market

The Hurst index is widely used to describe the long memory process of time series in economics, finance, and other fields. The setting for Hurst index estimation has not been thoroughly investigated by current literature. Many scholars choose the estimation settings subjectively without comparing the results of different settings or just choose the settings providing the desirable results. In this research, the impact of various settings such as correlation processing, trend processing, scale range selection, subsequence division, fitting method, and tail-cut method on the Hurst index estimation models, such as R/S and DFA, are evaluated through the Monte Carlo simulation. The results show that the settings have significant impact on the accuracy of the Hurst index estimation. The detailed optimal six setting for Hurst index estimation is summarized for future researchers. In addition, the results show that the comprehensive performance of the DFA estimation is better than the R/S-type estimation. On the basis of the optimal setting, the Hurst indexes of China's stock market are estimated. The daily volatility in the Chinese stock market show long memory by the Hurst index. Our contribution is to identify the optimal model setting for the Hurst index estimation by comparing all the six optional settings in every step of estimation. Our stepwise analysis for model effectiveness may shed light on challenges for various approaches to market trend analysis.