A central limit theorem is proved for the sample covariances of a linear process. The sufficient conditions for the theorem are described by more natural ones than usual. We apply this theorem to the parameter estimation of a fitted spectral model, which does not necessarily include the true spectral density of the linear process. We also deal with estimation problems for an autoregressive signal plus white noise. A general result is given for efficiency of Newton-Raphson iterations of the likelihood equation.
Publié le : 1982-03-14
Classification:
Stationary processes,
central limit theorem,
linear processes,
spectral density,
periodogram,
Gaussian maximum likelihood estimate,
robustness,
autoregressive signal with white noise,
Newton-Raphson iteration,
60F15,
62M15,
60G10,
60G35
@article{1176345696,
author = {Hosoya, Yuzo and Taniguchi, Masanobu},
title = {A Central Limit Theorem for Stationary Processes and the Parameter Estimation of Linear Processes},
journal = {Ann. Statist.},
volume = {10},
number = {1},
year = {1982},
pages = { 132-153},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345696}
}
Hosoya, Yuzo; Taniguchi, Masanobu. A Central Limit Theorem for Stationary Processes and the Parameter Estimation of Linear Processes. Ann. Statist., Tome 10 (1982) no. 1, pp. 132-153. http://gdmltest.u-ga.fr/item/1176345696/