Open Access
Translator Disclaimer
May, 1977 Asymptotic Behavior of Least-Squares Estimates for Autoregressive Processes with Infinite Variances
Victor J. Yohai, Ricardo A. Maronna
Ann. Statist. 5(3): 554-560 (May, 1977). DOI: 10.1214/aos/1176343855

Abstract

Let $y_t$ be an order $p$ autoregressive process of the form $y_t + \sum^p_{s=1} \beta_s y_{t-s} = u_t$, where the $u_t$'s are i.i.d. variables with a symmetric distribution $F$ such that $E \log^+ |u_t| < \infty$. For the Yule-Walker version $\beta_T^\ast$ of the least-squares estimate of $\beta = (\beta_1,\cdots, \beta_p)$, it is shown that $T^\frac{1}{2}(\beta_T^\ast - \beta)$ is bounded in probability.

Citation

Download Citation

Victor J. Yohai. Ricardo A. Maronna. "Asymptotic Behavior of Least-Squares Estimates for Autoregressive Processes with Infinite Variances." Ann. Statist. 5 (3) 554 - 560, May, 1977. https://doi.org/10.1214/aos/1176343855

Information

Published: May, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0378.62075
MathSciNet: MR436509
Digital Object Identifier: 10.1214/aos/1176343855

Subjects:
Primary: 62M10
Secondary: 62E20

Keywords: Asymptotic theory , autoregressive processes , infinite variance , least-squares estimates

Rights: Copyright © 1977 Institute of Mathematical Statistics

JOURNAL ARTICLE
7 PAGES


SHARE
Vol.5 • No. 3 • May, 1977
Back to Top