Abstract
Time series data, i.e., temporally ordered data, is routinely collected and analysed in in many fields of natural science, economy, technology and medicine, where it is of importance to verify the assumption of stochastic stationarity prior to modeling the data. Nonstationarities in the data are often attributed to structural changes with segments between adjacent change-points being approximately stationary. A particularly important, and thus widely studied, problem in statistics and signal processing is to detect changes in the mean at unknown time points. In this paper, we present the R package mosum, which implements elegant and mathematically well-justified procedures for the multiple mean change problem using the moving sum statistics.
Highlights
With its beginnings dating back as far as the 1950s (Page 1954), change-point analysis is still a very active field of research in statistics
We present the package mosum (Meier, Cho, and Kirch 2021), which provides an implementation of the moving sum (MOSUM) procedure from Eichinger and Kirch (2018) and its multiscale extension for offline detection of multiple changes in the mean
It is available for the statistical computing language R (R Core Team 2021) from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=mosum
Summary
With its beginnings dating back as far as the 1950s (Page 1954), change-point analysis is still a very active field of research in statistics. Several R packages implement algorithms based on global optimization of penalized cost functions, such as the package strucchange (Zeileis, Leisch, Hornik, and Kleiber 2002) for detecting structural changes in linear regression models (it contains utility functions for empirical MOSUM processes); changepoint (Killick and Eckley 2014) implementing the pruned exact linear time (PELT) algorithm (Killick, Fearnhead, and Eckley 2012a) (which implements the binary segmentation algorithm (Scott and Knott 1974; Sen and Srivastava 1975) and the segment neighborhood algorithm (Auger and Lawrence 1989; Bai and Perron 1998)); changepoint.np (Haynes and Killick 2020) extending the PELT algorithm with nonparametric cost functions; ecp (James and Matteson 2014) implementing the nonparametric change-point method for multivariate data from Matteson and James (2014); Segmentor3IsBack (Cleynen, Rigaill, and Koskas 2016) and fpop (Rigaill, Hocking, Maidstone, and Fearnhead 2019) implementing pruned dynamic programming algorithms using the functional pruning, see Rigaill (2015) and Maidstone, Hocking, Rigaill, and Fearnhead (2017) Another branch of methodologies performs multiscale analysis in searching for change-points in local environments (Fang, Li, and Siegmund 2020; Chan and Chen 2017). In Appendix, we discuss some algorithmic and implementation details (Section A), remark on the computational time of MOSUM-based procedures (Section B), and provide the proof of an asymptotic distributional result (Section C)
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