This note concerns the problem of order determination for autoregressive models. Rissanen's "Predictive least squares principle" prescribes that one should choose as order estimate $\hat{k}(n)$ at time $n$ the order of the model which has given the least mean square prediction error up to that time. We show that this procedure is strongly consistent, that is, that $\hat{k}(n) \rightarrow p$ a.s. as $n \rightarrow \infty$ when the data are generated by an AR process of order $p$, given an upper bound $p^\ast$.
Publié le : 1989-06-14
Classification:
Autoregressive process,
martingale difference,
order determination,
predictive least squares,
strong consistency,
structure identification,
62M10,
93E12,
60F15,
62M20
@article{1176347154,
author = {Hemerly, E. M. and Davis, M. H. A.},
title = {Strong Consistency of the PLS Criterion for Order Determination of Autoregressive Processes},
journal = {Ann. Statist.},
volume = {17},
number = {1},
year = {1989},
pages = { 941-946},
language = {en},
url = {http://dml.mathdoc.fr/item/1176347154}
}
Hemerly, E. M.; Davis, M. H. A. Strong Consistency of the PLS Criterion for Order Determination of Autoregressive Processes. Ann. Statist., Tome 17 (1989) no. 1, pp. 941-946. http://gdmltest.u-ga.fr/item/1176347154/