Non parametric resampling for stationary Markov processes: The local grid bootstrap approach

A new resampling technique, referred as “local grid bootstrap” (LGB), based on nonparametric local bootstrap and applicable to a wide range of stationary general space Markov processes is proposed. This nonparametric technique resamples local neighborhoods defined around the true samples of the observed multivariate time serie. The asymptotic behavior of this resampling procedure is studied in detail. Applications to linear and nonlinear (in particular chaotic) simulated time series are presented, and compared to Paparoditis and Politis [2002. J. Statist. Plan. Inf. 108, 301-328] approach, referred as “local bootstrap” (LB) and developed in earlier similar works. The method shows to be efficient and robust even when the length of the observed time series is reasonably small.