Robust Resampling Methods for Time Series

We study the robustness of block resampling procedures for time series. We first derive a set of formulas to quantify their quantile breakdown point. For the block bootstrap and the sub- sampling, we find a very low quantile breakdown point. A similar robustness problem arises in relation to data-driven methods for selecting the block size in applications, which can ren- der inferences based on standard resampling methods useless already in simple estimation and testing settings. To solve this problem, we introduce a robust fast resampling scheme that is applicable to a wide class of time series settings. Monte Carlo simulation and sensitivity analysis for the simple AR(1) model confirm the dramatic fragility of classical resampling procedures in presence of contaminations by outliers. They also show the better accuracy and effciency of the robust resampling approach under different types of data constellations.