B. Cooper Boniece, Lajos Horváth, Lorenzo Trapani
arXiv 7 Oct 2023 · Statistics — Methodology · publishedJournal of Econometrics (2025) · 3 citations (OpenAlex)
arXiv:2310.04853 · PDF · DOI · OpenAlex · Extracted main text
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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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Berkes, I., R. Gabrys, L. Horváth, and P. Kokoszka (2009) Detecting changes in the mean of functional observations | 1.000 | 9 | 4 | 100% |
| 2 | Horváth, L. and P. Kokoszka (2012) Inference for Functional Data with Applications | 1.000 | 6 | 4 | 100% |
| 3 | Berkes, I., L. Horváth, and G. Rice (2013) Weak invariance principles for sums of dependent random functions | 1.000 | 6 | 3 | 100% |
| 4 | Andrews, D. W (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation | 0.928 | 4 | 3 | 100% |
| 5 | Horváth, L. and G. Rice (2023) Changepoint detection in time series | 0.874 | 8 | 2 | 100% |
| 6 | Happ, C. and S. Greven (2018) Multivariate functional principal component analysis for data observed on different (dimensional) domains | 0.737 | 3 | 2 | 100% |
| 7 | Hörmann, S. and P. Kokoszka (2010) Weakly dependent functional data | 0.737 | 3 | 2 | 100% |
| 8 | Matteson, D. S. and N. A. James (2014) A nonparametric approach for multiple change point analysis of multivariate data | 0.737 | 3 | 2 | 100% |
| 9 | Rice, G. and C. Zhang (2022) Consistency of binary segmentation for multiple change-point estimation with functional data | 0.737 | 3 | 2 | 100% |
| 10 | Biau, G., K. Bleakley, and D. M. Mason (2016) Long signal change-point detection | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 69 scored citations.