We define, in a dynamic framework, the notions of binding functions, i
mages, reflecting sets, indirect identification, indirect information,
and encompassing. We study the properties of the notion of encompassi
ng when the true distribution does not necessarily belong to one of th
e two competing models of interest. In this context we propose various
test procedures of the encompassing hypothesis. Some of these procedu
res are based on simulations, and some of them are linked with the not
ion of indirect estimation (in particular, the GET and simulated GET p
rocedures). As a by-product, we get an asymptotic theory of the tests
of non-nested hypotheses in the stationary dynamic case.