Two-stage data segmentation permitting multiscale change points, heavy tails and dependence

Haeran Cho*, Claudia Kirch

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

The segmentation of a time series into piecewise stationary segments is an important problem both in time series analysis and signal processing. In the presence of multiscale change points with both large jumps over short intervals and small jumps over long intervals, multiscale methods achieve good adaptivity but require a model selection step for removing false positives and duplicate estimators. We propose a
localised application of the Schwarz criterion, which is applicable with any multiscale candidate generating procedure fulfilling mild assumptions, and establish its theoretical consistency in estimating the number and locations of multiple change points under general assumptions permitting heavy tails and dependence. In particular, combined with a MOSUM-based candidate generating procedure, it attains minimax rate optimality in both detection lower bound and localisation for i.i.d. sub-Gaussian errors. Overall competitiveness of the proposed methodology compared to existing methods is shown through its theoretical and numerical performance.
Original languageEnglish
Number of pages32
JournalAnnals of the Institute of Statistical Mathematics
Volume2021
Early online date25 Sep 2021
DOIs
Publication statusE-pub ahead of print - 25 Sep 2021

Bibliographical note

Funding Information:
Haeran Cho was supported by the EPSRC grant no. EP/N024435/1. The authors would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme ‘Statistical scalability’ (supported by EPSRC grant number EP/R014604/1) when work on this paper was undertaken.

Publisher Copyright:
© 2021, The Institute of Statistical Mathematics, Tokyo.

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