Estimating Hurst Index Based On Wavelet

Long range persistence has been observed in many fields. A variety of methods have been proposed to estimate Hurst index of non-stationary and stationary process, which has power-law decay. In this paper, non-stationary process (fractional Brownian motion) is transformed to a stationary process and the autocorrelation decay exponentially by using discrete wavelet transformation. Then a novel unbiased estimator is developed. Wavelet method not only effectively eliminates the trend of series, but also deals with the abrupt change of series. Even the series contains some noise, wavelet method can perform well. At last, by comparing with R/H method, we conclude that estimator based on wavelet is more robust and more exact than that on R/H.