Bootstrap Methods for Time Series

The chapter gives a review of the literature on bootstrap methods for time series data. It describes various possibilities on how the bootstrap method, initially introduced for independent random variables, can be extended to a wide range of dependent variables in discrete time, including parametric or nonparametric time series models, autoregressive and Markov processes, long range dependent time series and nonlinear time series, among others. Relevant bootstrap approaches, namely the intuitive residual bootstrap and Markovian bootstrap methods, the prominent block bootstrap methods as well as frequency domain resampling procedures, are described. Further, conditions for consistent approximations of distributions of parameters of interest by these methods are presented. The presentation is deliberately kept non-technical in order to allow for an easy understanding of the topic, indicating which bootstrap scheme is advantageous under a specific dependence situation and for a given class of parameters of interest. Moreover, the chapter contains an extensive list of relevant references for bootstrap methods for time series.