Additive outliers in INAR(1) models

In this paper the integer-valued autoregressive model of order one, con1 taminated with additive outliers is studied in some detail. Moreover, parameter estima2 tion is also addressed. Supposing that the timepoints of the outliers are known but their 3 sizes are unknown, we prove that the conditional least squares (CLS) estimators of the 4 offspring and innovation means are strongly consistent. In contrast, however, the CLS 5 estimators of the outliers’ sizes are not strongly consistent, although they converge to 6 a random limit with probability 1. We also prove that th joint CLS estimator of the 7 offspring and innovation means is asymptotically normal. Conditionally on the values 8 of the process at the timepoints neighboring to the outliers’ occurrences, the joint CLS 9 estimator of the sizes of the outliers is also asymptotically normal. 10 M. Barczy (B) · M. Ispány Faculty of Informatics, University of Debrecen, Pf. 12, Debrecen 4010, Hungary e-mail: [email protected] M. Ispány e-mail: [email protected] G. Pap University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, Szeged 6720, Hungary e-mail: [email protected] M. Scotto Departamento de Matemática, Campus Universitário de Santiago, Universidade de Aveiro, 3810-193 Aveiro, Portugal e-mail: [email protected] M. E. Silva Faculdade de Economia, Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200 464 Porto, Portugal e-mail: [email protected] 123 Journal: 362 Article No.: 0398 TYPESET DISK LE CP Disp.:2011/7/12 Pages: 15 Layout: Small-X A u th o r P r o o f