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The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models. (English) Zbl 1200.62105

Summary: 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M09 Non-Markovian processes: estimation
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
62G20 Asymptotic properties of nonparametric inference
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