Change detection in INAR(p) processesagainst various alternative hypotheses

Pap, Gyula and T. Szabó, Tamás (2013) Change detection in INAR(p) processesagainst various alternative hypotheses. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 42 (7). pp. 1386-1405. ISSN 0361-0926

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Abstract

Change in the coefficients or in the mean of the innovation of an INAR(p) process is a sign of distur-bance that is important to detect. The proposed methods can test for change in any one of these quantitiesseparately, or in any collection of them. They make both one-sided and two-sided tests possible, further-more, they can be used to test against the ‘epidemic’ alternative. The tests are based on a CUSUM processusing CLS estimators of the parameters. Under the one-sided and two-sided alternatives consistency ofthe tests is proved and the properties of the change-point estimator are also explored.Keywords: Change-point detection; stable INAR(p) process.

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