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
发表期刊	PHYSICAL REVIEW E
	2009-12-01
卷号	80 期号:6
文章类型	Article
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.
关键词	Fractals Gaussian Noise Maximum Likelihood Estimation Mean Square Error Methods Monte Carlo Methods Piecewise Polynomial Techniques
WOS标题词	Science & Technology ; Physical Sciences
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研究方向	Physics
WOS类目	Physics, Fluids & Plasmas ; Physics, Mathematical
WOS记录号	WOS:000273228000042
引用统计	被引频次：12[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.ia.ac.cn/handle/173211/3126
专题	脑图谱与类脑智能实验室_脑网络组研究
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
第一作者单位	模式识别国家重点实验室
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).