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Block Bootstrap for the Empirical Process of Long‐Range Dependent Data
Author(s) -
Tewes Johannes
Publication year - 2018
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12256
Subject(s) - mathematics , limit (mathematics) , resampling , range (aeronautics) , nuisance parameter , nonparametric statistics , monotonic function , central limit theorem , goodness of fit , gaussian process , statistics , econometrics , gaussian , estimator , mathematical analysis , materials science , physics , quantum mechanics , composite material
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.