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Preprint
On changepoint detection in functional data using empirical energy distance
07 Oct 2023
Abstract
We propose a novel family of test statistics to detect the presence of
changepoints in a sequence of dependent, possibly multivariate,
functional-valued observations. Our approach allows to test for a very general
class of changepoints, including the "classical" case of changes in the mean,
and even changes in the whole distribution. Our statistics are based on a
generalisation of the empirical energy distance; we propose weighted
functionals of the energy distance process, which are designed in order to
enhance the ability to detect breaks occurring at sample endpoints. The
limiting distribution of the maximally selected version of our statistics
requires only the computation of the eigenvalues of the covariance function,
thus being readily implementable in the most commonly employed packages, e.g.
R. We show that, under the alternative, our statistics are able to detect
changepoints occurring even very close to the beginning/end of the sample. In
the presence of multiple changepoints, we propose a binary segmentation
algorithm to estimate the number of breaks and the locations thereof.
Simulations show that our procedures work very well in finite samples. We
complement our theory with applications to financial and temperature data.
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Details
- Title
- On changepoint detection in functional data using empirical energy distance
- Creators
- B. Cooper BonieceLajos HorváthLorenzo Trapani
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021861874104721