Asymptotic normality of the maximum likelihood estimator for the parameters of a long range dependent Gaussian process is proved. Furthermore, the limit of the Fisher information matrix is derived for such processes which implies efficiency of the estimator and of an approximate maximum likelihood estimator studied by Fox and Taqqu. The results are derived by using asymptotic properties of Toeplitz matrices and an equicontinuity property of quadratic forms.
Publié le : 1989-12-14
Classification:
Long range dependence,
fractional ARMA,
maximum likelihood estimation,
efficiency,
Toeplitz forms,
62F12,
60F99,
62M10
@article{1176347393,
author = {Dahlhaus, Rainer},
title = {Efficient Parameter Estimation for Self-Similar Processes},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 1749-1766},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347393}
}
Dahlhaus, Rainer. Efficient Parameter Estimation for Self-Similar Processes. Ann. Statist., Tome 17 (1989) no. 1, pp. 1749-1766. http://gdmltest.u-ga.fr/item/1176347393/