A strongly dependent Gaussian sequence has a spectral density $f(x, \theta)$ satisfying $f(x, \theta) \sim |x|^{-\alpha(\theta)} L_\theta(x)$ as $x \rightarrow 0$, where $0 < \alpha(\theta) < 1$ and $L_\theta(x)$ varies slowly at 0. Here $\theta$ is a vector of unknown parameters. An estimator for $\theta$ is proposed and shown to be consistent and asymptotically normal under appropriate conditions. These conditions are satisfied by fractional Gaussian noise and fractional ARMA, two examples of strongly dependent sequences.
Publié le : 1986-06-14
Classification:
Strong dependence,
long-range dependence,
maximum likelihood estimation,
fractional Gaussian noise,
fractional ARMA,
62F12,
60F99,
62M10
@article{1176349936,
author = {Fox, Robert and Taqqu, Murad S.},
title = {Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series},
journal = {Ann. Statist.},
volume = {14},
number = {2},
year = {1986},
pages = { 517-532},
language = {en},
url = {http://dml.mathdoc.fr/item/1176349936}
}
Fox, Robert; Taqqu, Murad S. Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series. Ann. Statist., Tome 14 (1986) no. 2, pp. 517-532. http://gdmltest.u-ga.fr/item/1176349936/