Bernoulli

  • Bernoulli
  • Volume 15, Number 2 (2009), 297-324.

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

Feike C. Drost, Ramon van den Akker, and Bas J.M. Werker

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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.

Article information

Source
Bernoulli, Volume 15, Number 2 (2009), 297-324.

Dates
First available in Project Euclid: 4 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.bj/1241444892

Digital Object Identifier
doi:10.3150/08-BEJ153

Mathematical Reviews number (MathSciNet)
MR2543864

Zentralblatt MATH identifier
1200.62105

Keywords
branching process with immigration integer-valued time series local-to-unity asymptotics near unit root Poisson limit experiment

Citation

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 15 (2009), no. 2, 297--324. doi:10.3150/08-BEJ153. https://projecteuclid.org/euclid.bj/1241444892


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