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...

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...

The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data. The methods that are available for implementing the bootstrap and the accuracy of bootstrap estimates depend on whether the data are a random...

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...

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...

We provide a consistent specification test for GARCH(1,1) models based on a test statistic of Cramér-von Mises type. Since the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model-based...

The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z2. This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. The paper explores the range of...

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...

We propose a general bootstrap procedure to approximate the null distribution of nonparametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy to verify conditions, we establish asymptotic validity of the proposed bootstrap procedure....

We develop some asymptotic theory for applications of block bootstrap resampling schemes to multivariate integrated and cointegrated time series. It is proved that a multivariate, continuous-path block bootstrap scheme applied to a full rank integrated process, succeeds in estimating...