Title: Relevant changes in eigensystems of functional time series
Authors: Tim Kutta - Ruhr-Universität Bochum (Germany) [presenting]
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Abstract: Detecting structural changes in time dependent data is a prominent topic in statistical literature. However not all trends in the data are important in applications, but only those of large enough influence. We examine the eigenfunctions and eigenvalues of covariance kernels of $L_2[0,1]$-valued stationary time series for relevant changes. By self normalization techniques we derive pivotal, asymptotically consistent tests for relevant changes and consider their finite sample properties in a simulation study. The investigation of German annual temperature data demonstrates the applicability of our approach.