This article considers testing for mean-level shifts in functional data. The class of the famous Darling-Erdős-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 finitedimensional subspaces. We discuss suitable estimates and demonstrate empirically that altogether this change-point procedure performs well under moderate temporal dependence.Moreover, Darling-Erdős-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.

We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on weighted denoising estimates, involving the group fused LASSO, and on the weighted CUSUM estimates. Due to the fixed sample size, the common weighting schemes do not guarantee consistency under (serial) dependence and most typical weightings do not even provide consistency in the i.i.d. setting when the noise is too dominant.Hence, on the one hand, we propose a consistent covariance-based extension of existing weighting schemes and discuss straightforward estimates of those weighting schemes. The performance will be demonstrated empirically in a simulation study. On the other hand, we derive sharp bounds on the change to noise ratio that ensure consistency in the i.i.d. setting for classical weightings.