Specification test for Markov models with measurement errors

Most existing works on specification testing assume that we have direct observations from the model of interest. We study specification testing for Markov models based on contaminated observations. The evolving model dynamics of the unobservable Markov chain is implicitly coded into the conditional distribution of the observed process. To test whether the underlying Markov chain follows a parametric model, we propose measuring the deviation between nonparametric and parametric estimates of conditional regression functions of the observed process. Specifically, we construct a nonparametric simultaneous confidence band for conditional regression functions and check whether the parametric estimate is contained within the band.