  This article extends the autoregressive count time series model class by
allowing for a model with regimes, that is, some of the parameters in the model
depend on the state of an unobserved Markov chain. We develop a quasi-maximum
likelihood estimator by adapting the extended Hamilton-Grey algorithm for the
Poisson log-linear autoregressive model, and we perform a simulation study to
check the finite sample behaviour of the estimator. The motivation for the
model comes from the study of corporate defaults, in particular the study of
default clustering. We provide evidence that time series of counts of US
monthly corporate defaults consists of two regimes and that the so-called
contagion effect, that is current defaults affect the probability of other
firms defaulting in the future, is present in one of these regimes, even after
controlling for financial and economic covariates. We further find evidence for
that the covariate effects are different in each of the two regimes. Our
results imply that the notion of contagion in the default count process is
time-dependent, and thus more dynamic than previously believed.
