Geodesic
New approach to the segmentation problem for time series of arbitrary nature
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 61-74
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We consider the problem of splitting time series of arbitrary nature (stochastic, deterministic, or mixed) into segments generated by the same mechanism. We introduce a new concept of $\in$-complexity of continuous functions and give a characterization of this quantity for Hölder continuous functions. On the basis of the $\in$-complexity parameters, we propose a new technique for the segmentation of time series that does not require any a priori knowledge of how these series were generated. 
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B. S. Darhovsky; A. Piryatinska. New approach to the segmentation problem for time series of arbitrary nature. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Stochastic calculus, martingales, and their applications, Tome 287 (2014), pp. 61-74. http://geodesic.mathdoc.fr/item/TM_2014_287_a3/

[1] Khodadadi A., Asgharian M., Change-point problem and regression: An annotated bibliography, E-print. COBRA Preprint Ser., Paper 44, 2008 http://biostats.bepress.com/cobra/art44

[2] Shiryaev A.N., “O stokhasticheskikh modelyakh i optimalnykh metodakh v zadachakh skoreishego obnaruzheniya”, Teoriya veroyatn. i ee primen., 53:3 (2008), 417–436 | DOI | MR

[3] Shiryaev A.N., “Quickest detection problems: Fifty years later”, Sequential Anal., 29 (2010), 345–385 | DOI | MR | Zbl

[4] Brodsky B.E., Darkhovsky B.S., Non-parametric statistical diagnosis: Problems and methods, Kluwer, Dordrecht, 2000 | MR | Zbl

[5] Darkhovskii B.S., Kaplan A.Ya., Shishkin S.L., “O podkhode k otsenke slozhnosti krivykh (na primere elektroentsefalogrammy cheloveka)”, Avtomatika i telemekhanika, 2002, no. 3, 134–140

[6] Darkhovsky B., Piryatinska A., “Quickest detection of changes in the generating mechanism of a time series via the $\epsilon $-complexity of continuous functions”, Sequential Anal., 33 (2014), 231–250 | DOI | MR | Zbl

[7] Kolmogorov A.N., “Kombinatornye osnovaniya teorii informatsii i ischisleniya veroyatnostei”, UMN, 38:4 (1983), 27–36 | MR | Zbl

[8] Kolmogorov A.N., Fomin S.V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1968 | MR | Zbl

[9] Darkhovsky B., Piryatinska A., “A new complexity-based algorithmic procedures for electroencephalogram (EEG) segmentation”, Signal processing in medicine and biology symposium (SPMB), 2012, IEEE, 2012, 1–5 | DOI