Outliers in INAR(1) models
نویسندگان
چکیده
In this paper the integer-valued autoregressive model of order one, contaminated with additive or innovational outliers is studied in some detail, parameter estimation is also addressed. In particular, the asymptotic behavior of conditional least squares (CLS) estimators is analyzed. We suppose that the time points of the outliers are known, but their sizes are unknown. It is proved that the CLS estimators of the offspring and innovation means are strongly consistent, but the CLS estimators of the sizes of the outliers are not strongly consistent; nevertheless, 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. 2000 Mathematics Subject Classifications : 60J80, 62F12.
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