TY - JOUR
T1 - The dependent wild bootstrap
AU - Shao, Xiaofeng
N1 - Funding Information:
Xiaofeng Shao is Assistant Professor, Department of Statistics, University of Illinois at Urbana–Champaign, Champaign, IL 61820 (E-mail: [email protected]). The author is very grateful to an anonymous referee for many constructive comments that led to substantial improvement of the article. The author thanks the editor and an associate editor for providing helpful suggestions, and Jim Miller for providing the data set used in this work. The research was supported in part by National Science Foundation grants DMS-0804937 and DMS-0724752.
PY - 2010/3
Y1 - 2010/3
N2 - We propose a new resampling procedure, the dependent wild bootstrap, for stationary time series. As a natural extension of the traditional wild bootstrap to time series setting, the dependent wild bootstrap offers a viable alternative to the existing block-based bootstrap methods, whose properties have been extensively studied over the last two decades. Unlike all of the block-based bootstrap methods, the dependent wild bootstrap can be easily extended to irregularly spaced time series with no implementational difficulty. Furthermore, it preserves the favorable bias and mean squared error property of the tapered block bootstrap, which is the state-of-the-art block-based method in terms of asymptotic accuracy of variance estimation and distribution approximation. The consistency of the dependent wild bootstrap in distribution approximation is established under the framework of the smooth function model. In addition, we obtain the bias and variance expansions of the dependent wild bootstrap variance estimator for irregularly spaced time series on a lattice. For irregularly spaced nonlattice time series, we prove the consistency of the dependent wild bootstrap for variance estimation and distribution approximation in the mean case. Simulation studies and an empirical data analysis illustrate the finite-sample performance of the dependent wild bootstrap. Some technical details and tables are included in the online supplemental material.
AB - We propose a new resampling procedure, the dependent wild bootstrap, for stationary time series. As a natural extension of the traditional wild bootstrap to time series setting, the dependent wild bootstrap offers a viable alternative to the existing block-based bootstrap methods, whose properties have been extensively studied over the last two decades. Unlike all of the block-based bootstrap methods, the dependent wild bootstrap can be easily extended to irregularly spaced time series with no implementational difficulty. Furthermore, it preserves the favorable bias and mean squared error property of the tapered block bootstrap, which is the state-of-the-art block-based method in terms of asymptotic accuracy of variance estimation and distribution approximation. The consistency of the dependent wild bootstrap in distribution approximation is established under the framework of the smooth function model. In addition, we obtain the bias and variance expansions of the dependent wild bootstrap variance estimator for irregularly spaced time series on a lattice. For irregularly spaced nonlattice time series, we prove the consistency of the dependent wild bootstrap for variance estimation and distribution approximation in the mean case. Simulation studies and an empirical data analysis illustrate the finite-sample performance of the dependent wild bootstrap. Some technical details and tables are included in the online supplemental material.
KW - Block bootstrap
KW - Irregularly spaced time series
KW - Lag window estimator
KW - Tapering
KW - Variance estimation
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U2 - 10.1198/jasa.2009.tm08744
DO - 10.1198/jasa.2009.tm08744
M3 - Article
AN - SCOPUS:77952570020
SN - 0162-1459
VL - 105
SP - 218
EP - 235
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 489
ER -