Moving Block and Tapered Block Bootstrap for Functional Time Series with an Application to the K-Sample Mean Problem
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We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block and the tapered block bootstrap and show that these block bootstrap procedures also provide consistent estimators of the spectral density operator of the underlying functional process at frequency zero. Furthermore, we consider block bootstrap-based procedures for fully functional testing of the equality of mean functions between several independent functional time series. We establish the validity of the block bootstrap methods in approximating the distribution of the statistic of interest under the null. The finite sample behaviour of the procedures is investigated by means of simulations. An application to a real-life dataset is also discussed.
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