The Local Bootstrap for Markov processes

A nonparametric bootstrap procedure is proposed for stochastic processes which follow a general autoregressive structure. The procedure generates bootstrap replicates by locally resampling the original set of observations reproducing automatically its dependence properties. It avoids an initial nonparametric estimation of process characteristics in order to generate the pseudo-time series and the bootstrap replicates mimic several of the properties of the original process. Applications of the procedure in nonlinear time series analysis are considered and theoretically justi ed; some simulated and real data examples are discussed. AMS 1990 subject classi cations: Primary 62G09, 62M05; secondary 62M10.