Asymptotic Behaviour of Estimators of the Parameters of Nearly Unstable INAR(1) Models
نویسندگان
چکیده
A sequence of first–order integer–valued autoregressive type (INAR(1)) processes is investigated, where the autoregressive type coefficients converge to 1. It is shown that the limiting distribution of the joint conditional least squares estimators for this coefficient and for the mean of the innovation is normal. Consequences for sequences of Galton–Watson branching processes with unobservable immigration, where the mean of the offspring distribution converges to 1 (which is the critical value), are discussed.
منابع مشابه
Asymptotic Inference for Nearly Unstable Inar(1) Models
The first–order integer–valued autoregressive (INAR(1)) process is investigated, where the autoregressive coefficient is close to one. It is shown that the limiting distribution of the conditional least–squares estimator for this coefficient is normal and, in contrast to the familiar AR(1) process, the rate of convergence is n. Finally, the nearly critical Galton–Watson process with unobservabl...
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