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January, 1974 Estimation of Models of Autoregressive Signal Plus White Noise
Marcello Pagano
Ann. Statist. 2(1): 99-108 (January, 1974). DOI: 10.1214/aos/1176342616


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.


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Marcello Pagano. "Estimation of Models of Autoregressive Signal Plus White Noise." Ann. Statist. 2 (1) 99 - 108, January, 1974.


Published: January, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0317.62059
MathSciNet: MR347021
Digital Object Identifier: 10.1214/aos/1176342616

Keywords: 6255 , 6285 , Autoregressive-moving average , Gauss-Newton , non-linear regression , spectral averages

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 1 • January, 1974
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