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This article is cited in 17 scientific papers (total in 17 papers)
New approach to the segmentation problem for time series of arbitrary nature
B. S. Darhovskya, A. Piryatinskab a Institute of Systems Analysis, Russian Academy of Sciences, Moscow, Russia
b Department of Mathematics, San Francisco State University, San Francisco, CA 94132, USA
Abstract:
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.
Received in April 2014
Citation:
B. S. Darhovsky, A. Piryatinska, “New approach to the segmentation problem for time series of arbitrary nature”, Stochastic calculus, martingales, and their applications, Collected papers. Dedicated to Academician Albert Nikolaevich Shiryaev on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 287, MAIK Nauka/Interperiodica, Moscow, 2014, 61–74; Proc. Steklov Inst. Math., 287:1 (2014), 54–67
Linking options:
https://www.mathnet.ru/eng/tm3585https://doi.org/10.1134/S0371968514040049 https://www.mathnet.ru/eng/tm/v287/p61
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