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
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
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