Block Bootstrap for the Empirical Process of Long†Range Dependent Data

Johannes Tewes

Journal of Time Series Analysis, 2018, vol. 39, issue 1, 28-53

Abstract: We consider the bootstrapped empirical process of long†range dependent data. It is shown that this process converges to a semi†degenerate limit, where the random part of this limit is always Gaussian. Thus the bootstrap might fail when the original empirical process accomplishes a noncentral limit theorem. However, even in this case our results can be used to estimate a nuisance parameter that appears in the limit of many nonparametric tests under long memory. Moreover, we develop a new resampling procedure for goodness†of†fit tests and a test for monotonicity of transformations.

Date: 2018
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