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In this paper, we consider the structural change in a class of discrete valued time series, where the true conditional distribution of the observations is assumed to be unknown. The conditional mean of the process depends on a parameter $ \theta ^* $ θ ∗ 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 increments of a Browninan 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. [ABSTRACT FROM AUTHOR]

This paper deals with model selection for a general class of integer-valued time series. We propose a penalized criterion based on the Poisson quasi-likelihood of the model. Under certain regularity conditions, the consistency of the procedure as well as the consistency and the asymptotic normality of the Poisson quasi-likelihood estimator of the selected model are established. Simulation experiments are conducted for some classical models such as the Poisson and negative binomial model with linear and nonlinear dynamics. Also, an application to a real dataset is provided. [ABSTRACT FROM AUTHOR]