Detecting structural breaks in eigensystems of functional time series

11/18/2019
by   Holger Dette, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/12/2020

Detecting relevant differences in the covariance operators of functional time series – a sup-norm approach

In this paper we propose statistical inference tools for the covariance ...
04/09/2018

Structural break analysis for spectrum and trace of covariance operators?

This paper deals with analyzing structural breaks in the covariance oper...
09/13/2019

Two-sample tests for relevant differences in the eigenfunctions of covariance operators

This paper deals with two-sample tests for functional time series data, ...
03/09/2022

Detecting relevant changes in the spatiotemporal mean function

For a spatiotemporal process {X_j(s,t) |  s ∈ S , t ∈ T }_j =1, … , n, w...
04/09/2020

Pivotal tests for relevant differences in the second order dynamics of functional time series

Motivated by the need to statistically quantify differences between mode...
12/15/2020

Proofs and additional experiments on Second order techniques for learning time-series with structural breaks

We provide complete proofs of the lemmas about the properties of the reg...