We address the nonparametric model validation problem for hidden Markov models with partially observable variables and hidden states. We achieve this goal by constructing a nonparametric simultaneous confidence envelope for transition density function of the observable variables and checking...

We study nonparametric inference of stochastic models driven by stable Lévy processes. We introduce a nonparametric estimator of the stable index that achieves the parametric rate of convergence. For the volatility function, due to the heavy-tailedness, the classical least-squares method is not...

This article studies density and parameter estimation problems for nonlinear parametric models with conditional heteroscedasticity. We propose a simple density estimate that is particularly useful for studying the stationary density of nonlinear time series models. Under a general dependence...