A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series
成果类型：
Article
署名作者：
Moulines, E.; Roueff, F.; Taqqu, M. S.
署名单位：
IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Boston University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/07-AOS527
发表日期：
2008
页码：
1925-1956
关键词：
摘要：
We consider a time series X = (X-k, k is an element of Z) with memory parameter d(0) is an element of R. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the local Whittle wavelet estimator of the memory parameter d(0). This is a wavelet-based semiparametric pseudo-likelihood maximum method estimator. The estimator may depend on a given finite range of scales or on a range which becomes infinite with the sample size. We show that the estimator is consistent and rate optimal if X is a linear process, and is asymptotically normal if X is Gaussian.