Abstract
We show that the linear process bootstrap (LPB) and the autoregressive sieve bootstrap (AR sieve) are, in general, not valid for statistics whose large-sample distribution depends on moments of order higher than two, irrespective of whether the data come from a linear time series or not. Inspired by the block-of-blocks bootstrap, we circumvent this non-validity by applying the LPB and AR sieve to suitably blocked data and not to the original data itself. In a simulation study, we compare the LPB, AR sieve, and moving block bootstrap applied directly and to blocked data.
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