Bootstrap confidence bands for the autoregression function
- Kreiss, Jens-Peter
- Neumann, Michael H.
2010 Mathematics Subject Classification
- 62G07 62M05 62G09 62G15
- Nonparametric autoregression, nonparametric regression, strong approximation, bootstrap, wild bootstrap, confidence bands
We derive a strong approximation of a local polynomial estimator (LPE) in nonparametric autoregression by an LPE in a corresponding nonparametric regression model. This generally suggests the application of regression-typical tools for statistical inference in nonparametric autoregressive models. It provides an important simplification for the bootstrap method to be used: It is enough to mimic the structure of a nonparametric regression model rather than to imitate the more complicated process structure in the autoregressive case. As an example we consider a simple wild bootstrap. Besides our particular application to simultaneous confidence bands, this suggests the validity of wild bootstrap for several other statistical purposes.