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Higher-Order Improvements Of The Parametric Bootstrap For Long-Memory Gaussian Processes, Donald W.K. Andrews, Offer Lieberman
Higher-Order Improvements Of The Parametric Bootstrap For Long-Memory Gaussian Processes, Donald W.K. Andrews, Offer Lieberman
Cowles Foundation Discussion Papers
This paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d 0 are included. The results establish that the bootstrap provides higher-order improvements over the delta method. Analogous results are given for tests. The CIs and tests are based on one or other of two approximate maximum likelihood estimators. The first estimator solves the first-order conditions with respect to the covariance parameters of a “plug-in” log-likelihood function that has the unknown mean replaced by the sample mean. The second …
The Block-Block Bootstrap: Improved Asymptotic Refinements, Donald W.K. Andrews
The Block-Block Bootstrap: Improved Asymptotic Refinements, Donald W.K. Andrews
Cowles Foundation Discussion Papers
The asymptotic refinements attributable to the block bootstrap for time series are not as large as those of the nonparametric iid bootstrap or the parametric bootstrap. One reason is that the independence between the blocks in the block bootstrap sample does not mimic the dependence structure of the original sample. This is the join-point problem. In this paper, we propose a method of solving this problem. The idea is not to alter the block bootstrap. Instead, we alter the original sample statistics to which the block bootstrap is applied. We introduce block statistics that possess join-point features that are similar …