A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing
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Date
2013-06-27
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Abstract
Two key ingredients to carry out inference on the copula of multivariate observations
are the empirical copula process and an appropriate resampling scheme for
the latter. Among the existing techniques used for i.i.d. observations, the multiplier
bootstrap of R emillard and Scaillet (2009) frequently appears to lead to inference
procedures with the best finite-sample properties. Buecher and Ruppert (2013) recently
proposed an extension of this technique to strictly stationary strongly mixing
observations by adapting the dependent multiplier bootstrap of Buehlmann (1993,
Section 3.3) to the empirical copula process. The main contribution of this work is
a generalization of the multiplier resampling scheme proposed by Buecher and Ruppert
(2013) along two directions. First, the resampling scheme is now genuinely
sequential, thereby allowing to transpose to the strongly mixing setting all of the
existing multiplier tests on the unknown copula, including nonparametric tests for
change-point detection. Second, the resampling scheme is now fully automatic as a
data-adaptive procedure is proposed which can be used to estimate the bandwidth
(block length) parameter. A simulation study is used to investigate the finitesample
performance of the resampling scheme and provides suggestions on how to
choose several additional parameters. As by-products of this work, the weak convergence
of the sequential empirical copula process is obtained under many serial
dependence conditions, and the validity of a sequential version of the dependent
multiplier bootstrap for empirical processes of Buehlmann is obtained under weaker
conditions on the strong mixing coefficients and the multipliers.
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Keywords
lag window estimator, multiplier central limit theorem, multivariate observations, partial-sum process, ranks, serial dependence