A fast estimation algorithm on the Hurst parameter of discrete-time fractional Brownian motion

The purpose of this paper is to demonstrate that the discrete-time fractional Gaussian noise (DFGN) is a regular process. Based on this property, a fast algorithm with low computational cost is proposed to estimate the Hurst parameter H, which is an important parameter in fractional Brownian motion (FBM). This algorithm is robust under amplitude shift, invariant to time shift, and unaffected by a scaling factor in power spectral density (PSD). Finally, the computational complexity is also investigated.