## The Annals of Statistics

### Asymptotic Behavior of Least-Squares Estimates for Autoregressive Processes with Infinite Variances

#### 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.

#### Article information

Source
Ann. Statist., Volume 5, Number 3 (1977), 554-560.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176343855

Digital Object Identifier
doi:10.1214/aos/1176343855

Mathematical Reviews number (MathSciNet)
MR436509

Zentralblatt MATH identifier
0378.62075

JSTOR