Poisson limit of an inhomogeneous nearly critical INAR(1) model

Györfi, László and Ispány, Márton and Pap, Gyula and Varga, Katalin (2007) Poisson limit of an inhomogeneous nearly critical INAR(1) model. Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum, 73 (3-4). pp. 783-809. ISSN 0001-6969

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Abstract

An inhomogeneous first-order integer-valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient converges to one and the immigration mean tends to zero at appropriate speeds. It is shown that the process converges weakly to a Poisson or a compound Poisson distribution.

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