Kernel Matching Scheme for Block Bootstrap of Time Series Data

The block bootstrap for time series consists in randomly resampling blocks of the original data with replacement and aligning these blocks into a bootstrap sample. Recently, several matching schemes for the block bootstraps have been suggested to improve its performance by reduction of bias [Bernoulli 4 (1998), 305]. The matching schemes are usually achieved by aligning with higher likelihood those blocks which match at their ends. The kernel matching scheme we consider here takes some of the dependence structure of the data into account and is based on a kernel estimate of the conditional lag one distribution. In this article, transition probabilities of the kernel matching scheme are investigated in detail by concentrating on a simple case. Our results here discuss theoretical properties of the transition probability matrix including ergodicity, which shows the potential of the matching scheme for bias reduction