Bootstrapping nonparametric estimators of the volatility function

We prove that the bootstrap works in a quite general sense for nonparametric estimators of the trend and volatility functions in nonlinear AR-ARCH-models. We illustrate the implications of this result by constructing uniform confidence bands for those functions based on localized nonparametric function estimates. As an application, we study the trend and volatility of a time series of high frequency foreign exchange rate returns.