Detecting structural breaks in eigensystems of functional time series

Dette, H. and Kutta, T.

Volume: 15 Pages: 944-983
DOI: 10.1214/20-EJS1796
Published: 2021

Detecting structural changes in functional 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. In this paper we address the problem of identifying relevant changes in the eigenfunctions and eigenvalues of covariance kernels of L2[0, 1]-valued time series. By selfnormalization techniques we derive pivotal, asymptotically consistent tests for relevant changes in these characteristics of the second order structure and investigate their finite sample properties in a simulation study. The applicability of our approach is demonstrated analyzing German annual temperature data. © 2021, Institute of Mathematical Statistics. All rights reserved.

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