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Bernoulli

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

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

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.

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

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bj/1241444892
Digital Object Identifier: doi:10.3150/08-BEJ153
Mathematical Reviews number (MathSciNet): MR2543864

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