The Annals of Statistics
- Ann. Statist.
- Volume 19, Number 3 (1991), 1155-1162.
Convergence of Moments of Least Squares Estimators for the Coefficients of an Autoregressive Process of Unknown Order
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.
Ann. Statist., Volume 19, Number 3 (1991), 1155-1162.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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