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Two key ingredients to carry out inference on the copula of multivariateobservations are the empirical copula process and an appropriate resamplingscheme for the latter. Among the existing techniques used for i.i.d.observations, the multiplier bootstrap of R\'{e}millard and Scaillet (J.Multivariate Anal. 100 (2009) 377-386) frequently appears to lead to inferenceprocedures with the best finite-sample properties. B\"{u}cher and Ruppert (J.Multivariate Anal. 116 (2013) 208-229) recently proposed an extension of thistechnique to strictly stationary strongly mixing observations by adapting thedependent multiplier bootstrap of B\"{u}hlmann (The blockwise bootstrap in timeseries and empirical processes (1993) ETH Z\"{u}rich, Section 3.3) to theempirical copula process. The main contribution of this work is ageneralization of the multiplier resampling scheme proposed by B\"{u}cher andRuppert along two directions. First, the resampling scheme is now genuinelysequential, thereby allowing to transpose to the strongly mixing setting manyof the existing multiplier tests on the unknown copula, including nonparametrictests for change-point detection. Second, the resampling scheme is now fullyautomatic as a data-adaptive procedure is proposed which can be used toestimate the bandwidth parameter. A simulation study is used to investigate thefinite-sample performance of the resampling scheme and provides suggestions onhow to choose several additional parameters. As by-products of this work, thevalidity of a sequential version of the dependent multiplier bootstrap forempirical processes of B\"{u}hlmann is obtained under weaker conditions on thestrong mixing coefficients and the multipliers, and the weak convergence of thesequential empirical copula process is established under many serial dependenceconditions.

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing