Asymptotic Behavior of Least-Squares Estimates for Autoregressive Processes with Infinite Variances
Yohai, Victor J. ; Maronna, Ricardo A.
Ann. Statist., Tome 5 (1977) no. 1, p. 554-560 / Harvested from Project Euclid
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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.
Publié le : 1977-05-14
Classification:  Autoregressive processes,  least-squares estimates,  infinite variance,  asymptotic theory,  62M10,  62E20 
@article{1176343855,
     author = {Yohai, Victor J. and Maronna, Ricardo A.},
     title = {Asymptotic Behavior of Least-Squares Estimates for Autoregressive Processes with Infinite Variances},
     journal = {Ann. Statist.},
     volume = {5},
     number = {1},
     year = {1977},
     pages = { 554-560},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176343855}
}

Yohai, Victor J.; Maronna, Ricardo A. Asymptotic Behavior of Least-Squares Estimates for Autoregressive Processes with Infinite Variances. Ann. Statist., Tome 5 (1977) no. 1, pp.  554-560. http://gdmltest.u-ga.fr/item/1176343855/