Innovational Outliers in INAR(1) Models

• Published in: Communications in statistics. Theory and methods Vol. 39; no. 18; pp. 3343 - 3362
• Main Authors: Barczy, Mátyás, Ispány, Márton, Pap, Gyula, Scotto, Manuel, Eduarda Silva, Maria
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.01.2010; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Conditional asymptotic normality; Conditional least squares estimators; Distribution theory; Exact sciences and technology; General topics; INAR; Innovational outliers; Mathematical models; Mathematics; Multivariate analysis; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Statistics; Stochastic processes; Strong consistency; Studies; Time series; Discriminant analysis; Conditional distribution; Statistical distribution; Strong consistency; 60J80; Conditional asymptotic normality; Autoregressive model; Multivariate analysis; Statistical method; Integer; Outlier; Innovational outliers; INAR; Least squares method; Asymptotic normality; Point process; 62F12; Conditional least squares estimators
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920903259831

We consider integer-valued autoregressive models of order one contaminated with innovational outliers. Assuming that the time points of the outliers are known but their sizes are unknown, we prove that Conditional Least Squares (CLS) estimators of the offspring and innovation means are strongly consistent. In contrast, CLS estimators of the outliers' sizes are not strongly consistent. 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 time points preceding the outliers' occurrences, the joint CLS estimator of the sizes of the outliers is asymptotically normal.