Valid Resampling of Higher Order Statistics Using Linear Process Bootstrap and Autoregressive Sieve Bootstrap
نویسنده
چکیده
Abstract. In this paper we show that the linear process bootstrap (LPB) and the autoregressive sieve bootstrap (AR sieve) fail in general for statistics whose large-sample distribution depends on higher order features of the dependence structure rather than just on autocovariances. We discuss why this is still the case under linearity if it does not come along with causality and invertibility with respect to an i.i.d. white noise. Inspired by the block-of-blocks bootstrap, in order to circumvent this non-validity we propose to apply the LPB and AR sieve not directly to the observations but to suitably blocked data. In a simulation study, we compare LPB, AR sieve and moving block bootstrap (MBB) applied directly and to blocked data.
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