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.
- Non-parametric kernel estimator
- Nonlinear autoregressive process
- Primary: 62G08, 62M05
- Secondary: 62F40
- Stationary bootstrap procedure