Testing Parameter Change in General Integer-Valued Time Series

We consider the structural change in a class of discrete valued time series, which the conditional distribution belongs to the one-parameter exponential family. We propose a change point test based on the maximum likelihood estimator of the model's parameter. Under the null hypothesis (of no change), the test statistic converges to a well-known distribution, allowing the calculation of the critical value of the test. The test statistic diverges to infinity under the alternative, meaning that the test has asymptotic power one. Some simulation results and real data applications are reported to show the effectiveness of the proposed procedure.