The multiple filter test for change point detection in time series
The authors investigate an unknown number of change points in the expectation occurring on multiple time scales in time series with general distributional assumption in which other parameters are allowed to change and propose a multiple filter test (MFT) for the detection of change point in the expectation in sequence of random variables. Their approach is based on the translation of the framework for change point detection that was designed for point processes (see [\textit{M. Messer} et al., Ann. Appl. Stat. 8, No. 4, 2027--2067 (2014; Zbl 1454.62365)]) to a model that is based on piecewise sequences of i.i.d. random variables. The proposed procedure starts with the formulation of the MOSUM (moving-sum) process which includes a parameter estimating auxiliary process and then, it is investigated an asymptotic setting in which MOSUM process converges weakly to a functional \(L\) of a standard Brownian motion, which depends only on the window size. This procedure extends other methods given by \textit{L. Horváth} et al. [J. Stat. Plann. Inference 138, No. 6, 1894--1904 (2008; Zbl 1131.62037)], \textit{B. Eichinger} and \textit{C. Kirch} [Bernoulli 24, No. 1, 526--564 (2018; Zbl 1388.62251)], \textit{K. Frick} et al. [``Multiscale change point inference'', J. R. Statist. Soc. B 76, No. 3, 495--500 (2014; \url{doi:10.1111/rssb.12047})], \textit{P. Fryzlewicz} [Ann. Stat. 42, No. 6, 2243--2281 (2014; Zbl 1302.62075)] or \textit{D. S. Matteson} and \textit{N. A. James} [J. Am. Stat. Assoc. 109, No. 505, 334--345 (2014; Zbl 1367.62260)]. Finally, they show robustness of the proposed procedure against changes in other distributional parameters if there is no change in expectation. Also, a function implementing the described test and change point estimation is given and is available in the R package MFT.
scientific article; zbMATH DE number 6931814
scientific article