Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version K Mukherjee, Bootstrapping M-estimators in generalized autoregressive conditional heteroscedastic models, Biometrika, Volume 107, Issue 3, September 2020, Pages 753–760, is available online at: https://academic.oup.com/biomet/article-abstract/107/3/753/5831314
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Bootstrapping M-estimators in GARCH models
AU - Mukherjee, Kanchan
N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biometrika following peer review. The definitive publisher-authenticated version K Mukherjee, Bootstrapping M-estimators in generalized autoregressive conditional heteroscedastic models, Biometrika, Volume 107, Issue 3, September 2020, Pages 753–760, is available online at: https://academic.oup.com/biomet/article-abstract/107/3/753/5831314
PY - 2020/9/1
Y1 - 2020/9/1
N2 - We consider the weighted bootstrap approximation of the distribution of a class of M-estimators of the GARCH (p, q) parameters. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator which is asymptotically normal. We propose an algorithm for the computation of M-estimates which at the same time is software-friendly to compute the bootstrap replicates from the given data. Our simulation study indicates superior coverage rates for various weighted bootstrap schemes compared with the rates based on the normal approximation and the existing bootstrap methods in the literature such as percentile t-subsampling schemes for the GARCH model. Since some familiar bootstrap schemes are special cases of the weighted bootstrap, this paper thus provides a unified theory and algorithm for bootstrapping in GARCH models.
AB - We consider the weighted bootstrap approximation of the distribution of a class of M-estimators of the GARCH (p, q) parameters. We prove that the bootstrap distribution, given the data, is a consistent estimate in probability of the distribution of the M-estimator which is asymptotically normal. We propose an algorithm for the computation of M-estimates which at the same time is software-friendly to compute the bootstrap replicates from the given data. Our simulation study indicates superior coverage rates for various weighted bootstrap schemes compared with the rates based on the normal approximation and the existing bootstrap methods in the literature such as percentile t-subsampling schemes for the GARCH model. Since some familiar bootstrap schemes are special cases of the weighted bootstrap, this paper thus provides a unified theory and algorithm for bootstrapping in GARCH models.
KW - GARCH model
KW - M-estimation
KW - Weighted bootstrap
U2 - 10.1093/biomet/asaa023
DO - 10.1093/biomet/asaa023
M3 - Journal article
VL - 107
SP - 753
EP - 760
JO - Biometrika
JF - Biometrika
SN - 0006-3444
IS - 3
ER -