We consider time series $Y_t = G(X_t)$ where $X_t$ is Gaussian
with long memory and $G$ is a polynomial. The series $Y_t$ may or may not have
long memory. The spectral density $g_\theta(x)$ of $Y_t$ is parameterized by a
vector $\theta$ and we want to estimate its true value $\theta_0$ . We use a
least-squares Whittle-type estimator $\hat{\theta}_N$ for $\theta_0$, based on
observations $Y_1,\dots,Y_N$. If $Y_t$ is Gaussian, then
$\sqrt{N}(\hat{\theta}_N-\theta_0)$ converges to a Gaussian distribution. We
show that for non-Gaussian time series $Y_t$ , this $\sqrt{N}$ consistency of
the Whittle estimator does not always hold and that the limit is not
necessarily Gaussian. This can happen even if $Y_t$ has short memory.
Publié le : 1999-03-14
Classification:
Hermite polynomials,
non-central limit theorem,
long-range dependence,
quadratic forms,
time series,
62E20,
62F10,
60G18
@article{1018031107,
author = {Giraitis, Liudas and Taqqu, Murad S.},
title = {Whittle estimator for finite-variance non-Gaussian time series
with long memory},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 178-203},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031107}
}
Giraitis, Liudas; Taqqu, Murad S. Whittle estimator for finite-variance non-Gaussian time series
with long memory. Ann. Statist., Tome 27 (1999) no. 4, pp. 178-203. http://gdmltest.u-ga.fr/item/1018031107/