Additive outliers in INAR(1) models

Mátyás Barczy (), Márton Ispány (), Gyula Pap (), Manuel Scotto () and Maria Silva ()

Statistical Papers, 2012, vol. 53, issue 4, 935-949

Abstract: In this paper the integer-valued autoregressive model of order one, contaminated with additive outliers is studied in some detail. Moreover, parameter estimation is also addressed. Supposing that the timepoints 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. We also prove that the joint CLS estimator of the offspring and innovation means is asymptotically normal. Conditionally on the values of the process at the timepoints neighboring to the outliers’ occurrences, the joint CLS estimator of the sizes of the outliers is also asymptotically normal. Copyright Springer-Verlag 2012

Keywords: Integer-valued autoregressive models; Additive outliers; Conditional least squares estimators; Strong consistency; Conditional asymptotic normality; 60J80; 62F12 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s00362-011-0398-x

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