This paper considers non-negative integer-valued autoregressive processes where the autoregression parameter is close to unity. We consider the asymptotics of this ‘near unit root’ situation. The local asymptotic structure of the likelihood ratios of the model is obtained, showing that the limit experiment is Poissonian. To illustrate the statistical consequences we discuss efficient estimation of the autoregression parameter and efficient testing for a unit root.
Publié le : 2009-05-15
Classification:
branching process with immigration,
integer-valued time series,
local-to-unity asymptotics,
near unit root,
Poisson limit experiment
@article{1241444892,
author = {Drost, Feike C. and van den Akker, Ramon and Werker, Bas J.M.},
title = {The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models},
journal = {Bernoulli},
volume = {15},
number = {1},
year = {2009},
pages = { 297-324},
language = {en},
url = {http://dml.mathdoc.fr/item/1241444892}
}
Drost, Feike C.; van den Akker, Ramon; Werker, Bas J.M. The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models. Bernoulli, Tome 15 (2009) no. 1, pp. 297-324. http://gdmltest.u-ga.fr/item/1241444892/