  In this paper the integer-valued autoregressive model of order one,
contaminated with additive or innovational outliers is studied in some detail.
Moreover, parameter estimation is also addressed. Supposing that the time
points of the outliers are known but their sizes are unknown, we prove that the
Conditional Least Squares (CLS) estimators of the offspring and innovation
means are strongly consistent. In contrast, however, the CLS estimators of the
outliers' sizes are not strongly consistent, although they converge to a random
limit with probability 1. This random limit depends on the values of the
process at the outliers' time points and on the values at the preceding time
points and in case of additive outliers also on the values at the following
time points. We also prove that the joint CLS estimator of the offspring and
innovation means is asymptotically normal. Conditionally on the above described
values of the process, the joint CLS estimator of the sizes of the outliers is
also asymptotically normal.
