Speeding up estimation of the Hurst exponent by a two-stage procedure from a large to small range

Purpose - The Hurst exponent has been very important in telling the difference between fractal signals and explaining their significance. For estimators of the Hurst exponent, accuracy and efficiency are two inevitable considerations. The main purpose of this study is to raise the execution efficiency of the existing estimators, especially the fast maximum likelihood estimator (MLE), which has optimal accuracy. Design/methodology/approach - A two-stage procedure combining a quicker method and a more accurate one to estimate the Hurst exponent from a large to small range will be developed. For the best possible accuracy, the data-induction method is currently ideal for the first-stage estimator and the fast MLE is the best candidate for the second-stage estimator. Findings - For signals modeled as discrete-time fractional Gaussian noise, the proposed two-stage estimator can save up to 41.18 per cent the computational time of the fast MLE while remaining almost as accurate as the fast MLE, and even for signals modeled as discrete-time fractional Brownian motion, it can also save about 35.29 per cent except for smaller data sizes. Originality/value - The proposed two-stage estimation procedure is a novel idea. It can be expected that other fields of parameter estimation can apply the concept of the two-stage estimation procedure to raise computational performance while remaining almost as accurate as the more accurate of two estimators.