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arXiv · 1202.1617

Asymptotic behavior of CLS estimators for unstable INAR(2) models

Matyas Barczy·Marton Ispany·Gyula Pap
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Abstract

In this paper the asymptotic behavior of the conditional least squares estimators of the autoregressive parameters $(\alpha,\beta)$, of the stability parameter $\varrho := \alpha + \beta$, and of the mean $\mu$ of the innovation $\vare_k$, $k \in \NN$, for an unstable integer-valued autoregressive process $X_k = \alpha \circ X_{k-1} + \beta \circ X_{k-2} + \vare_k$, $k \in \NN$, is described. The limit distributions and the scaling factors are different according to the following three cases: (i) decomposable, (ii) indecomposable but not positively regular, and (iii) positively regular models.

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Matyas Barczy, Marton Ispany, Gyula Pap. 2012-02-08. Asymptotic behavior of CLS estimators for unstable INAR(2) models. https://arxiv.org/abs/1202.1617

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