Testing, encompassing, and simulating dynamic econometric models

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