• 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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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.

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

First available in Project Euclid: 4 May 2009

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


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.

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