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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
@article{TM_2014_287_a3,
     author = {B. S. Darhovsky and A. Piryatinska},
     title = {New approach to the segmentation problem for time series of arbitrary nature},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {61--74},
     publisher = {mathdoc},
     volume = {287},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2014_287_a3/}
}
TY  - JOUR
AU  - B. S. Darhovsky
AU  - A. Piryatinska
TI  - New approach to the segmentation problem for time series of arbitrary nature
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2014
SP  - 61
EP  - 74
VL  - 287
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2014_287_a3/
LA  - ru
ID  - TM_2014_287_a3
ER  - 
%0 Journal Article
%A B. S. Darhovsky
%A A. Piryatinska
%T New approach to the segmentation problem for time series of arbitrary nature
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2014
%P 61-74
%V 287
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2014_287_a3/
%G ru
%F TM_2014_287_a3
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