Change detection in INAR(p) processes against various alternative hypotheses

TL;DR

This paper develops statistical tests for detecting changes in the parameters or mean of INAR(p) processes, using CUSUM methods and conditional least squares estimators, with proven consistency and large sample properties.

Contribution

It introduces flexible change detection tests for INAR(p) processes that can identify changes in multiple parameters or the mean, including temporary changes, with theoretical guarantees.

Findings

Tests are consistent under alternative hypotheses.

Large sample properties of change-point estimators are established.

Methods enable one-sided and temporary change detection.

Abstract

Change in the coefficients or in the mean of the innovation distribution of an INAR(p) process is a sign of disturbance that is important to detect. The methods of this paper can test for change in any one of these quantities separately, or in any collection of them. They are available in forms that make one-sided tests possible, furthermore, they can be used to test for a temporary change. The tests are based on a CUSUM process using conditional least squares estimators of the parameters. Under alternative hypotheses consistency of the tests is proved and the large sample properties of the change-point estimator are also explored.