The Annals of Statistics

Convergence of Moments of Least Squares Estimators for the Coefficients of an Autoregressive Process of Unknown Order

R. J. Bhansali and F. Papangelou

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Abstract

Given a realization of $T$ consecutive observations of a stationary autoregressive process of unknown, possibly infinite, order $m$, it is assumed that a process of arbitrary finite order $p$ is fitted by least squares. Under appropriate conditions it is known that the estimators of the autoregressive coefficients are asymptotically normal. The question considered here is whether the moments of the (scaled) estimators converge, as $T \rightarrow \infty$, to the moments of their asymptotic distribution. We establish a general result for stationary processes (valid, in particular, in the Gaussian case) which is sufficient to imply this convergence.

Article information

Source
Ann. Statist., Volume 19, Number 3 (1991), 1155-1162.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348243

Digital Object Identifier
doi:10.1214/aos/1176348243

Mathematical Reviews number (MathSciNet)
MR1126319

Zentralblatt MATH identifier
0729.62082

JSTOR
links.jstor.org

Subjects
Primary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62M15: Spectral analysis 60G10: Stationary processes 60G15: Gaussian processes 60G25: Prediction theory [See also 62M20]

Keywords
Stationary process time series prediction uniform integrability convergence of moments

Citation

Bhansali, R. J.; Papangelou, F. Convergence of Moments of Least Squares Estimators for the Coefficients of an Autoregressive Process of Unknown Order. Ann. Statist. 19 (1991), no. 3, 1155--1162. doi:10.1214/aos/1176348243. https://projecteuclid.org/euclid.aos/1176348243


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