Year: 2021
Type: article
Abstract: The segmentation of data into stationary stretches also known as multiple change point problem is important for many applications in time series analysis as well as signal processing.Based on strong invariance principles, we analyze data segmentation methodology using moving sum (MOSUM) statistics for a class of regime-switching multivariate processes where each switch results in a change in the drift.In particular, this framework includes the data segmentation of multivariate partial sum, integrated diffusion and renewal processes even if the distance between change points is sublinear.We study the asymptotic behavior of the corresponding change point estimators, show consistency and derive the corresponding localization rates which are minimax optimal in a variety of situations including an unbounded number of changes in Wiener processes with drift.Furthermore, we derive the limit distribution of the change point estimators for local changes -a result that can in principle be used to derive confidence intervals for the change points.
Source: Statistica Sinica
Authors: Claudia Kirch, Philipp Klein
Institution: Otto-von-Guericke-Universität Magdeburg
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: bronze
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W4200329282