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.
This paper generalizes the negative binomial integer-valued GARCH model (NBINGARCH) to a negative binomial mixture integer-valued GARCH (NB-MINGARCH) for modeling time series of counts with presence of overdispersion. This class of models consists of a mixture of K stationary or non-stationary negative binomial integer-valued GARCH components. The advantage of these models over the NBINGARCH models includes the ability to handle multimodality and nonstationary components. Compared to the MINGARCH models, this class of models is more flexible to describe the greater degrees of overdispersion. The necessary and sufficient first and second order stationarity conditions are investigated. The estimation of parameters is done through an EM algorithm and the model is selected by some information criterions. Some simulation results and real data application are provided.
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