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

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  • Johannes Tewes

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.

Suggested Citation

  • Johannes Tewes, 2018. "Block Bootstrap for the Empirical Process of Long†Range Dependent Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(1), pages 28-53, January.
  • Handle: RePEc:bla:jtsera:v:39:y:2018:i:1:p:28-53
    DOI: 10.1111/jtsa.12256
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    Cited by:

    1. Jan Beran & Sucharita Ghosh, 2020. "Estimating the Mean Direction of Strongly Dependent Circular Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 210-228, March.

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