Abstract
We consider the problems of estimation and testing in models with serially correlated discrete latent variables. A particular case of this is the time series regression model in which a discrete explanatory variable is measured with error. Test statistics are derived for detecting serial correlation in such a model. We then show that the likelihood function can be evaluated by a recurrence relation, and thus maximum likelihood estimation is computationally feasible. An illustrative example of these methods is given, followed by a brief discussion of their applicability to a Markov model of switching regressions.
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