We consider a time series X={Xk, k∈ℤ} with memory parameter d0∈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 d0. 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.
Publié le : 2008-08-15
Classification:
Long memory,
semiparametric estimation,
wavelet analysis,
62M15,
62M10,
62G05,
62G20,
60G18
@article{1216237304,
author = {Moulines, E. and Roueff, F. and Taqqu, M. S.},
title = {A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 1925-1956},
language = {en},
url = {http://dml.mathdoc.fr/item/1216237304}
}
Moulines, E.; Roueff, F.; Taqqu, M. S. A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series. Ann. Statist., Tome 36 (2008) no. 1, pp. 1925-1956. http://gdmltest.u-ga.fr/item/1216237304/