Double block bootstrap confidence intervals for dependent data

The block bootstrap confidence interval for dependent data can outperform the conventional normal approximation only with nontrivial studentization which, in the case of complicated statistics, calls for specialist treatment and often results in unstable endpoints. We propose two double block bootstrap approaches for improving the accuracy of the block bootstrap confidence interval under very general conditions. The first approach calibrates the nominal coverage level and the second calculates studentizing factors directly from a block bootstrap series without the need for nontrivial analytical treatment. We prove that the two approaches reduce the coverage error of the block bootstrap interval by an order of magnitude with simple tuning of block lengths at the two block bootstrapping levels. Empirical properties of the procedures are investigated by simulations and application to an econometric time series. © 2009 Biometrika Trust.