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We consider infinite-dimensional Hilbert space-valued random variables thatare assumed to be temporal dependent in a broad sense. We prove a central limittheorem for the moving block bootstrap and for the tapered block bootstrap, andshow that these block bootstrap procedures also provide consistent estimatorsof the long run covariance operator. Furthermore, we consider blockbootstrap-based procedures for fully functional testing of the equality of meanfunctions between several independent functional time series. We establishvalidity of the block bootstrap methods in approximating the distribution ofthe statistic of interest under the null and show consistency of the blockbootstrap-based tests under the alternative. The finite sample behaviour of theprocedures is investigated by means of simulations. An application to areal-life dataset is also discussed.

Moving Block and Tapered Block Bootstrap for Functional Time Series with an Application to the K-Sample Mean Problem