  This article considers testing for mean-level shifts in functional data. The
class of the famous Darling-Erd\H{o}s-type cumulative sums (CUSUM) procedures
is extended to functional time series under short range dependence conditions
which are satisfied by functional analogues of many popular time series models
including the linear functional AR and the non-linear functional ARCH. We
follow a data driven, projection-based approach where the lower-dimensional
subspace is determined by (long run) functional principal components which are
eigenfunctions of the long run covariance operator. This second-order structure
is generally unknown and estimation is crucial - it plays an even more
important role than in the classical univariate setup because it generates the
finite-dimensional subspaces. We discuss suitable estimates and demonstrate
empirically that altogether this change-point procedure performs well under
moderate temporal dependence.
  Moreover, Darling-Erd\H{o}s-type change-point estimates based on (long run)
functional principal components as well as the corresponding "fully-functional"
counterparts are provided and the testing procedure is finally applied to
publicly accessible electricity data from a German power company.
