A framework for the detection of change points in the expectation in sequences of random variables is presented. Specifically, we investigate time series with general distributional assumptions that may show an unknown number of change points in the expectation occurring on multiple time scales and that may also contain change points in other parameters. To that end we propose a multiple filter test (MFT) that tests the null hypothesis of constant expectation and, in case of rejection of the null hypothesis, an algorithm that estimates the change points.
The MFT has three important benefits. First, it allows for general distributional assumptions in the underlying model, assuming piecewise sequences of i.i.d. random variables, where also relaxations with regard to identical distribution or independence are possible. Second, it uses a MOSUM type statistic and an asymptotic setting in which the MOSUM process converges weakly to a functional of a Brownian motion which is then used to simulate the rejection threshold of the statistical test. This approach enables a simultaneous application of multiple MOSUM processes which improves the detection of change points that occur on different time scales. Third, we also show that the method is practically robust against changes in other distributional parameters such as the variance or higher order moments which might occur with or even without a change in expectation. A function implementing the described test and change point estimation is available in the R package MFT.
Change point Multiscale MOSUM MFT
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This work was supported by the German Federal Ministry of Education and Research (www.bmbf.de) within the framework of the e:Med research and funding concept (grant number 01ZX1404B to SA, MM and GS) and by the Priority Program 1665 of the Deutsche Forschungsgemeinschaft (grant number SCHN 1370/02-1 to MM and GS, www.dfg.de). We thank Solveig Plomer for helpful comments to the manuscript.
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Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Albert S, Messer M, Schiemann J, Roeper J, Schneider G (2017) Multi-scale detection of variance changes in renewal processes in the presence of rate change points. J Time Ser Anal 38(6):1028–1052MathSciNetCrossRefzbMATHGoogle Scholar
Frick K, Munk A, Sieling H (2014) Multiscale change point inference. J R Stat Soc Ser B Stat Methodol 76(3):495–580 (with 32 discussions by 47 authors and a rejoinder by the authors)MathSciNetCrossRefGoogle Scholar
Messer M, Kirchner M, Schiemann J, Roeper J, Neininger R, Schneider G (2014) A multiple filter test for change point detection in renewal processes with varying variance. Ann Appl Stat 8(4):2027–2067MathSciNetCrossRefzbMATHGoogle Scholar
Staude B, Grün S, Rotter S (2010) Higher-order correlations in non-stationary parallel spike trains: statistical modeling and inference. Front Comput Neurosci 4:16CrossRefGoogle Scholar
Zhang H, Dantu R, Cangussu J (2009) Change point detection based on call detail records. In: Intelligence and Security Informatics. Institute of Electrical and Electronics Engineers, New York, pp 55–60Google Scholar