  A new time series bootstrap scheme, the time frequency toggle
(TFT)-bootstrap, is proposed. Its basic idea is to bootstrap the Fourier
coefficients of the observed time series, and then to back-transform them to
obtain a bootstrap sample in the time domain. Related previous proposals, such
as the "surrogate data" approach, resampled only the phase of the Fourier
coefficients and thus had only limited validity. By contrast, we show that the
appropriate resampling of phase and magnitude, in addition to some smoothing of
Fourier coefficients, yields a bootstrap scheme that mimics the correct
second-order moment structure for a large class of time series processes. As a
main result we obtain a functional limit theorem for the TFT-bootstrap under a
variety of popular ways of frequency domain bootstrapping. Possible
applications of the TFT-bootstrap naturally arise in change-point analysis and
unit-root testing where statistics are frequently based on functionals of
partial sums. Finally, a small simulation study explores the potential of the
TFT-bootstrap for small samples showing that for the discussed tests in
change-point analysis as well as unit-root testing, it yields better results
than the corresponding asymptotic tests if measured by size and power.
