Suppose $\{X_n\}$ is a $p$th order autoregressive process with innovations in the domain of attraction of a stable law and the true order $p$ unknown. The estimate $\hat{p}$ of $p$ is chosen to minimize Akaike's information criterion over the integers $0, 1, \cdots, K$. It is shown that $\hat{p}$ is weakly consistent and the consistency is retained if $K \rightarrow \infty$ as $N \rightarrow \infty$ at a certain rate depending on the index of the stable law.
Publié le : 1989-06-14
Classification:
Akaike's information criterion,
autoregressive processes,
infinite variance,
stable law,
62M10,
62F12,
60G10
@article{1176347145,
author = {Knight, Keith},
title = {Consistency of Akaike's Information Criterion for Infinite Variance Autoregressive Processes},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 824-840},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347145}
}
Knight, Keith. Consistency of Akaike's Information Criterion for Infinite Variance Autoregressive Processes. Ann. Statist., Tome 17 (1989) no. 1, pp. 824-840. http://gdmltest.u-ga.fr/item/1176347145/