Matched-block bootstrap for dependent data

Abstract

The block bootstrap for time series consists in randomly resampling blocks of consecutive values of the given data and aligning these blocks into a bootstrap sample. Here we suggest improving the performance of this method by aligning with higher likelihood those blocks which match at their ends. This is achieved by resampling the blocks according to a Markov chain whose transitions depend on the data. The matching algorithms that we propose take some of the dependence structure of the data into account. They are based on a kernel estimate of the conditional lag one distribution or on a fitted autoregression of small order. Numerical and theoretical analysis in the case of estimating the variance of the sample mean show that matching reduces bias and, perhaps unexpectedly, has relatively little effect of variance. Our theory extends to the case of smooth functions of a vector mean.