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Asymptotic inference for nearly unstable INAR(1) models
Part of
M. Ispány, G. Pap, M. C. A. van Zuijlen
Journal:

Journal of Applied Probability / Volume 40 / Issue 3 / September 2003

Published online by Cambridge University Press:

14 July 2016, pp. 750-765

Print publication:

September 2003
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A sequence of first-order integer-valued autoregressive (INAR(1)) processes is investigated, where the autoregressive-type coefficient converges to 1. It is shown that the limiting distribution of the conditional least squares estimator for this coefficient is normal and the rate of convergence is n3/2. Nearly critical Galton–Watson processes with unobservable immigration are also discussed.

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Asymptotic inference for nearly unstable INAR(1) models