Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise

	Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise
	Liu, Yingjun 1,2; Liu, Yong2 ; Wang, Kun 2; Jiang, Tianzi2 ; Yang, Lihua 1
刊名	PHYSICAL REVIEW E
	2009-12-01
卷号	80 期号:6
关键词	fractals Gaussian noise maximum likelihood estimation mean square error methods Monte Carlo methods piecewise polynomial techniques
英文摘要	Fractional Gaussian noise (fGn) is an important and widely used self-similar process, which is mainly parametrized by its Hurst exponent (H). Many researchers have proposed methods for estimating the Hurst exponent of fGn. In this paper we put forward a modified periodogram method for estimating the Hurst exponent based on a refined approximation of the spectral density function. Generalizing the spectral exponent from a linear function to a piecewise polynomial, we obtained a closer approximation of the fGn's spectral density function. This procedure is significant because it reduced the bias in the estimation of H. Furthermore, the averaging technique that we used markedly reduced the variance of estimates. We also considered the asymptotical unbiasedness of the method and derived the upper bound of its variance and confidence interval. Monte Carlo simulations showed that the proposed estimator was superior to a wavelet maximum likelihood estimator in terms of mean-squared error and was comparable to Whittle's estimator. In addition, a real data set of Nile river minima was employed to evaluate the efficiency of our proposed method. These tests confirmed that our proposed method was computationally simpler and faster than Whittle's estimator.
WOS标题词	Science & Technology ; Physical Sciences
类目[WOS]	Physics, Fluids & Plasmas ; Physics, Mathematical
研究领域[WOS]	Physics
关键词[WOS]	LONG-RANGE DEPENDENCE ; TIME-SERIES ; BROWNIAN MOTIONS ; 1/F NOISE ; REGRESSION ; WAVELETS ; TEXTURE ; SPECTRA
收录类别	SCI
语种	英语
WOS记录号	WOS:000273228000042
内容类型	期刊论文
源URL	[http://ir.ia.ac.cn/handle/173211/3126]
专题	自动化研究所_脑网络组研究中心
作者单位	1.Sun Yat Sen Univ, Sch Math & Comp Sci, Guangzhou 510275, Guangdong, Peoples R China 2.Chinese Acad Sci, Inst Automat, Natl Lab Pattern Recognit, LIAMA Ctr Computat Med, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Yingjun,Liu, Yong,Wang, Kun,et al. Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise[J]. PHYSICAL REVIEW E,2009,80(6).
APA	Liu, Yingjun,Liu, Yong,Wang, Kun,Jiang, Tianzi,&Yang, Lihua.(2009).Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise.PHYSICAL REVIEW E,80(6).
MLA	Liu, Yingjun,et al."Modified periodogram method for estimating the Hurst exponent of fractional Gaussian noise".PHYSICAL REVIEW E 80.6(2009).