If $x(\bullet)$ is a time series which may be written as $x(t) = s(t) + n(t)$ where $t$ is an integer, $s(\bullet)$ an autoregressive signal of order $q$ and $n(\bullet)$ white noise, then the model has $q + 2$ parameters. These are (i) the $q$ autoregressive parameters (ii) the residual variance of the autoregressive scheme and (iii) the variance of the white noise. A method is proposed to estimate the $q + 2$ parameters. This method is based on analogies with regression theory and in the case of a normal series yields strongly consistent efficient estimators.
@article{1176342616,
author = {Pagano, Marcello},
title = {Estimation of Models of Autoregressive Signal Plus White Noise},
journal = {Ann. Statist.},
volume = {2},
number = {1},
year = {1974},
pages = { 99-108},
language = {en},
url = {http://dml.mathdoc.fr/item/1176342616}
}
Pagano, Marcello. Estimation of Models of Autoregressive Signal Plus White Noise. Ann. Statist., Tome 2 (1974) no. 1, pp. 99-108. http://gdmltest.u-ga.fr/item/1176342616/