An efficient estimator of Hurst exponent through an autoregressive model with an order selected by data induction

Abstract

The discrete-time fractional Gaussian noise (DFGN) has been proven to be a regular process. Therefore, an autoregressive (AR) model of an infinite order can describe DFGN based on Wold and Kolmogorov theorems. A fast estimation algorithm on the Hurst exponent of DFGN or discrete-time fractional Brownian motion (DFBM) has been proposed, but the algorithm did not consider the order selection of AR model. Recently, a Hurst exponent estimator based on an AR model with six existing methods of order selection has been proposed to raise the accuracy of estimating the Hurst exponent. Although the estimation accuracy has been confirmed to be better than the one without order selection, the estimator still requires computing all parameter sets through the Levinson algorithm. In order to lower computational cost, this paper proposes an efficient method of order selection, simply called data induction, which uses simulation data to induce an appropriate threshold of terminating the Levinson algorithm before computing all parameter sets. Experimental results show that the proposed data-induction method has a competitive advantage over six existing methods of order selection in terms of lowering computational cost and raising the accuracy.