The asymptotic structure of nearly unstable non negative integer-valued AR(1) models

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Abstract

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.
Original languageEnglish
Pages (from-to)297-324
JournalBernoulli
Volume15
Issue number2
Publication statusPublished - 2009

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Autoregression
Unit Root
Unstable
Non-negative
Integer
Efficient Estimation
Autoregressive Process
Likelihood Ratio
Testing
Model
Experiment

Cite this

@article{ac0494ae7a3243cab5b4dd25e7dcf880,
title = "The asymptotic structure of nearly unstable non negative integer-valued AR(1) models",
abstract = "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.",
author = "F.C. Drost and {van den Akker}, R. and B.J.M. Werker",
note = "Appeared earlier as CentER DP 2006-44 (revised title)",
year = "2009",
language = "English",
volume = "15",
pages = "297--324",
journal = "Bernoulli",
issn = "1350-7265",
publisher = "International Statistical Institute",
number = "2",

}

The asymptotic structure of nearly unstable non negative integer-valued AR(1) models. / Drost, F.C.; van den Akker, R.; Werker, B.J.M.

In: Bernoulli, Vol. 15, No. 2, 2009, p. 297-324.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - The asymptotic structure of nearly unstable non negative integer-valued AR(1) models

AU - Drost, F.C.

AU - van den Akker, R.

AU - Werker, B.J.M.

N1 - Appeared earlier as CentER DP 2006-44 (revised title)

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

M3 - Article

VL - 15

SP - 297

EP - 324

JO - Bernoulli

JF - Bernoulli

SN - 1350-7265

IS - 2

ER -