  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.
