Change Detection in INAR(p) Processes Against Various Alternative Hypotheses

Gyula Pap · Tamás T. Szabó

11 citations0/0 files storedCommunication in Statistics- Theory and Methods

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Advanced Statistical Process Monitoring Probability and Statistical Research Time Series Analysis and Forecasting

Abstract

Change in the coefficients or the mean of the innovation of an INAR(p) process is a sign of disturbance that is important to detect. The proposed methods can test for change in any one of these quantities separately, or in any collection of them. They make both one-sided and two-sided tests possible, furthermore, they can be used to test against the “epidemic” alternative. The tests are based on a CUSUM process using CLS estimators of the parameters. Under the one-sided and two-sided alternatives, consistency of the tests is proved and the properties of the change-point estimator are also explored.

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References

1997Limit theorems in change-point analysis 2007Change detection in autoregressive time series 1998Change-point in the mean of dependent observations 2006On the detection of changes in autoregressive time series I. Asymptotics 2009Parameter change test for random coefficient integer‐valued autoregressive processes with application to polio data analysis

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2022An empirical-likelihood-based structural-change test for INAR processes

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