WAVELET ESTIMATION OF THE LONG MEMORY PARAMETER FOR HERMITE POLYNOMIAL OF GAUSSIAN PROCESSES

被引:20
作者
Clausel, M. [1 ]
Roueff, F. [2 ]
Taqqu, M. S. [3 ]
Tudor, C. [4 ]
机构
[1] Univ Grenoble, Lab Jean Kuntzmann, CNRS, F-38041 Grenoble 9, France
[2] Telecom Paris, Inst Telecom, CNRS LTCI, F-75634 Paris 13, France
[3] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA
[4] Univ Lille 1, CNRS, UMR 8524, Lab Paul Painleve, F-59655 Villeneuve Dascq, France
基金
美国国家科学基金会;
关键词
Hermite processes; wavelet coefficients; wiener chaos; self-similar processes; long-range dependence; CENTRAL LIMIT-THEOREMS; TIME-SERIES; COEFFICIENTS; FUNCTIONALS; REGRESSION;
D O I
10.1051/ps/2012026
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long-memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener-Ito integral of order 2. This happens even if the original process is defined through a Hermite polynomial of order higher than 2.
引用
收藏
页码:42 / 76
页数:35
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