We consider a longitudinal system in which transitions between the states are governed by a discrete time finite state space stochastic process X. Our aim, using aggregated sample survey data of the form typically collected by official statistical agencies, is to undertake model based inference for the underlying process X. We will develop inferential techniques for continuing sample surveys of two distinct types. First, longitudinal surveys in which the same individuals are sampled in each

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... e of the survey. Second, cross-sectional surveys which sample the same population in successive cycles but with no attempt to track particular individuals from one cycle to the next. Some of the basic results have appeared in Davis et al (2001) and Davis et al (2002).¶ ...