We will first present an overview of different bootstrap methods for time series focusing on the type of processes or on statistics for which these methods can be succesfully applied. We then discuss two particular bootstrapmethods in more detail: the autoregressive sieve bootstrap and a new frequency domain wild bootstrap. For the AR-sieve bootstrap we develop asimple test for checking its validity and show that for certain classes of statistics, the range of validity of this linear bootstrap method goesfar beyond that of the linear processes class. Conerning frequency domain bootstrap procedures, we show that the new frequency domain wild-typebootstrap procedure imitates correctly also the fourth order structure of the underlying process, overcoming therefore, several of the limitations of existing time domain or frequency domain bootstrap methods.
