  We introduce a general class of autoregressive models for studying the
dynamic of multivariate binary time series with stationary exogenous
covariates. Using a high-level set of assumptions, we show that existence of a
stationary path for such models is almost automatic and does not require
parameter restrictions when the noise term is not compactly supported. We then
study in details statistical inference in a dynamic version of a multivariate
probit type model, as a particular case of our general construction. To avoid a
complex likelihood optimization, we combine pseudo-likelihood and pairwise
likelihood methods for which asymptotic results are obtained for a single path
analysis and also for panel data, using ergodic theorems for multi-indexed
partial sums. The latter scenario is particularly important for analyzing
absence-presence of species in Ecology, a field where data are often collected
from surveys at various locations. Our results also give a theoretical
background for such models which are often used by the practitioners but
without a probabilistic framework.
