A bootstrap methodology for the periodogram of a stationary process is proposed which is based on a combination of a time domain parametric and a frequency domain nonparametric bootstrap. The parametric fit is used to generate periodogram ordinates and imitate the essential features of the data...

For nonparametric autoregression, we investigate a model based bootstrap procedure ("autoregressive bootstrap") that mimics the complete dependence structure of the original time series. We give consistency results for uniform bootstrap confidence bands of the autoregression function based on...

A non-stationary regression model for financial returns is examined theoretically in this paper. Volatility dynamics are modelled both exogenously and deterministic, captured by a nonparametric curve estimation on equidistant centered returns. We prove consistency and asymptotic normality of a...

Kernel smoothing in nonparametric autoregressive schemes offers a powerful tool in modelling time series. In this paper it is shown that the bootstrap can be used for estimating the distribution of kernel smoothers. This can be done by mimicking the stochastic nature of the whole process in the...

We prove geometric ergodicity and absolute regularity of the nonparametric autoregressive bootstrap process. To this end, we revisit this problem for nonparametric autoregressive processes and give some quantitative conditions (i.e., with explicit constants) under which the mixing coefficients...

A non-stationary regression model for financial returns is examined theoretically. Volatility dynamics are modeled by nonparametric curve estimation on equidistant return vectors. We prove consistency and asymptotic normality of symmetric estimators and of one-sided estimators for variances and...

We propose a nonparametric test for checking parametric hypotheses about the stationary density of weakly dependent observations. The test statistic is based on the L2-distance between a nonparametric and a smoothed version of a parametric estimate of the stationary density. It can be shown that...