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Keywords:

  • branching process with immigration;
  • Bessel process;
  • conditional least squares estimator;
  • martingale;
  • unstable INAR(p) process

ABSTRACT

In this paper, the asymptotic behavior of the conditional least squares estimators of the autoregressive parameters, of the mean of the innovations, and of the stability parameter for unstable integer-valued autoregressive processes of order 2 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.