The Annals of Statistics

Estimation of Models of Autoregressive Signal Plus White Noise

Marcello Pagano

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Abstract

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 information

Source
Ann. Statist., Volume 2, Number 1 (1974), 99-108.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342616

Digital Object Identifier
doi:10.1214/aos/1176342616

Mathematical Reviews number (MathSciNet)
MR347021

Zentralblatt MATH identifier
0317.62059

JSTOR
links.jstor.org

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

Citation

Pagano, Marcello. Estimation of Models of Autoregressive Signal Plus White Noise. Ann. Statist. 2 (1974), no. 1, 99--108. doi:10.1214/aos/1176342616. https://projecteuclid.org/euclid.aos/1176342616


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