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 boot-strap 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, which is used for the construction of simultaneous confidence bands and nonparametric supremum-type tests.
"Regression-type inference in nonparametric autoregression." Ann. Statist. 26 (4) 1570 - 1613, August 1998. https://doi.org/10.1214/aos/1024691254