Nonparametric model validation under dependence has been an important yet difficult problem. We address this problem for hidden Markov models with partially observable variables and unobservable or hidden states. We achieve this goal by constructing nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking whether the parametrically implied density estimate is entirely contained within such an envelope. Our specification test procedure is motivated by a functional connection between the transition density of the observable variables and the Markov transition kernel of the unobservable states. We show that our approach is applicable for a variety of models widely used in financial econometrics, including continuous-time diffusion models, hyperbolic Levy motions, stochastic volatility models, nonlinear time series models, multivariate stochastic regression models, and models with measurement errors among others. The finite sample performance of the proposed method is studied through simulations.