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2021 Detecting structural breaks in eigensystems of functional time series
Holger Dette, Tim Kutta
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Electron. J. Statist. 15(1): 944-983 (2021). DOI: 10.1214/20-EJS1796

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 L2[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.

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Holger Dette. Tim Kutta. "Detecting structural breaks in eigensystems of functional time series." Electron. J. Statist. 15 (1) 944 - 983, 2021. https://doi.org/10.1214/20-EJS1796

Information

Received: 1 December 2019; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.1214/20-EJS1796

Subjects:
Primary: 62F05, 62M10

JOURNAL ARTICLE
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Vol.15 • No. 1 • 2021
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