Detecting structural breaks in eigensystems of functional time series
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Date
2019
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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 in
uence. 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.
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Keywords
functional time series, self-normalization, eigenvalues, eigenfunctions, relevant changes