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

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.Comment: 67 pages; the CLS estimator of the mean of the innovation has been adde

Asymptotic behavior of unstable INAR(p) processes

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR(p)) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR(p) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unstable autoregressive processes of order p. An application for Boston armed robberies data set is presented.Comment: 35 pages; corrected and extended version: a new section on an application for Boston armed robberies data set is adde

On subset integer-valued autoregressions

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The PINAR (1, 1_S) model

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A model for count time series with periodic two orders autoregressive structure

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