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September, 1991 Convergence of Moments of Least Squares Estimators for the Coefficients of an Autoregressive Process of Unknown Order
R. J. Bhansali, F. Papangelou
Ann. Statist. 19(3): 1155-1162 (September, 1991). DOI: 10.1214/aos/1176348243

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.

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R. J. Bhansali. F. Papangelou. "Convergence of Moments of Least Squares Estimators for the Coefficients of an Autoregressive Process of Unknown Order." Ann. Statist. 19 (3) 1155 - 1162, September, 1991. https://doi.org/10.1214/aos/1176348243

Information

Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0729.62082
MathSciNet: MR1126319
Digital Object Identifier: 10.1214/aos/1176348243

Subjects:
Primary: 62M20
Secondary: 60G10, 60G15, 60G25, 62M10, 62M15

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 3 • September, 1991
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