Efficiently implementing the maximum likelihood estimator for Hurst exponent
type: Item
instance of: scholarly article
title: Efficiently implementing the maximum likelihood estimator for Hurst exponent
zbMATH Open document ID: 1407.62067
DOI: 10.1155/2014/490568
author: Yen-Ching Chang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper aims to efficiently implement the maximum likelihood estimator (MLE) for Hurst exponent, a vital parameter embedded in the process of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN), via a combination of the Levinson algorithm and Cholesky decomposition. Many natural and biomedical signals can often be modeled as one of these two processes. It is necessary for users to estimate the Hurst exponent to differentiate one physical signal from another. Among all estimators for estimating the Hurst exponent, the maximum likelihood estimator (MLE) is optimal, whereas its computational cost is also the highest. Consequently, a faster but slightly less accurate estimator is often adopted. Analysis discovers that the combination of the Levinson algorithm and Cholesky decomposition can avoid storing any matrix and performing any matrix multiplication and thus save a great deal of computer memory and computational time. In addition, the first proposed MLE for the Hurst exponent was based on the assumptions that the mean is known as zero and the variance is unknown. In this paper, all four possible situations are considered: known mean, unknown mean, known variance, and unknown variance. Experimental results show that the MLE through efficiently implementing numerical computation can greatly enhance the computational performance.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 60G22
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 7016566
describes a project that uses: longmemo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/490568
OpenAlex ID: W2117587513
Wikidata QID: Q59067776
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description: scientific article; zbMATH DE number 7016566