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Asymptotic inference for nearly unstable INAR(1) models. (English) Zbl 1042.62080
Summary: A sequence of first-order integer-valued autoregressive (INAR(l)) 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 $n^{3/2}$. Nearly critical Galton-Watson processes with unobservable immigration are also discussed.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. (statistics) 62F12 Asymptotic properties of parametric estimators 62E20 Asymptotic distribution theory in statistics 60J80 Branching processes
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##### References:
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