A Comparative Study And Application Of The Hurst Parameter Estimators For CSI300

Hurst exponent firstly was founded and raised by H.E. Hurst in the course of the study of a dam design in1951, and later Mandelbrot introduced the concept of fractals and Fractal Brownian Motion that provides a rigorous mathematical foundation to Hurst exponent. Fractal theory provides new methods and theoretical framework for the capital market research. There are many methods to estimate Hurst exponent.In this paper, we mainly describes eight kinds, including the absolute method, time variance method, differential variance method, the residual variance method, R/S method, periodogram method, the modified periodogram method and Higuchi. Through data simulation and comparison of different methods of Hurst exponent estimation, we can verify that the the residual variance method has higher accuracy and better stability. Then we use residual variance method to analysis CSI300through static analysis and historical analysis of the Hurst exponent. The analysis shows that CSI300is a Fractal Market and the effectiveness of the CSI300becomes stronger.