## The Annals of Statistics

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

#### 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

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