In this paper, we consider the structural change in a class of discrete valued time series, which the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter $\theta^*$ which may change over time. We provide sufficient conditions for the consistency and the asymptotic normality of the Poisson quasi-maximum likelihood estimator (QMLE) of the model. We consider an epidemic change-point detection and propose a test statistic based on the QMLE of the parameter. Under the null hypothesis of a constant parameter (no change), the test statistic converges to a distribution obtained from a difference of two Brownian bridge. The test statistic diverges to infinity under the epidemic alternative, which establishes that the proposed procedure is consistent in power. The effectiveness of the proposed procedure is illustrated by simulated and real data examples.
翻译:在本文中,我们考虑了一组离散的有价值时间序列的结构变化,假设对观测结果的真正有条件分布是未知的。该过程的有条件平均值取决于一个参数$\theta ⁇ $,该参数可能会随时间变化而变化。我们为模型Poisson 准最大可能性估计值(QMLE)的一致性和无症状的正常性提供了充分的条件。我们考虑了流行病变化点检测,并根据参数的QMLE提出了测试统计数据。在不变参数(无变化)的无效假设下,测试统计数据与从两座布朗山桥差异(两座布朗山桥)获得的分布汇合在一起。测试统计数据与流行病替代品的无限性有差异,该变量确定拟议的程序具有一致性。模拟和真实数据实例说明了拟议程序的有效性。