Detecting structural breaks in eigensystems of functional time series

TL;DR

This paper develops self-normalized, asymptotically consistent tests to detect significant structural changes in the eigenfunctions and eigenvalues of covariance kernels in functional time series, with applications to temperature data.

Contribution

It introduces a novel self-normalization method for testing relevant changes in the second order structure of functional time series.

Findings

Tests are asymptotically pivotal and consistent.

Simulation studies show good finite sample performance.

Application to temperature data demonstrates practical utility.

Abstract

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 $L^2[0,1]$-valued time series. By self-normalization 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.