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Subsampling and block-based bootstrap methods have been used in a wide rangeof inference problems for time series. To accommodate the dependence, theseresampling methods involve a bandwidth parameter, such as subsampling windowwidth and block size in the block-based bootstrap. In empirical work, usingdifferent bandwidth parameters could lead to different inference results, butthe traditional first order asymptotic theory does not capture the choice ofthe bandwidth. In this article, we propose to adopt the fixed-b approach, asadvocated by Kiefer and Vogelsang (2005) in theheteroscedasticity-autocorrelation robust testing context, to account for theinfluence of the bandwidth on the inference. Under the fixed-b asymptoticframework, we derive the asymptotic null distribution of the p-values forsubsampling and the moving block bootstrap, and further propose a calibrationof the traditional small-b based confidence intervals (regions, bands) andtests. Our treatment is fairly general as it includes both finite dimensionalparameters and infinite dimensional parameters, such as marginal distributionfunction and normalized spectral distribution function. Simulation results showthat the fixed-b approach is more accurate than the traditional small-bapproach in terms of approximating the finite sample distribution, and that thecalibrated confidence sets tend to have smaller coverage errors than theuncalibrated counterparts.

Fixed-b Subsampling and Block Bootstrap: Improved Confidence Sets Based on P-value Calibration