Stationary bootstrapping for non-parametric estimator of nonlinear autoregressive model

We consider stationary bootstrap approximation of the non-parametric kernel estimator in a general kth-order nonlinear autoregressive model under the conditions ensuring that the nonlinear autoregressive process is a geometrically Harris ergodic stationary Markov process. We show that the stationary bootstrap procedure properly estimates the distribution of the non-parametric kernel estimator. A simulation study is provided to illustrate the theory and to construct confidence intervals, which compares the proposed method favorably with some other bootstrap methods.