RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Chebyshevskii Sb., 2019, Volume 20, Issue 3, Pages 92–106 (Mi cheb800)  

Stochastic trends based on fuzzy mathematics

S. M. Agayana, Sh. R. Bogoutdinovab, D. A. Kamaevc, M. N. Dobrovolskya

a Geophysical Center RAS (Moscow)
b Schmidt Institute of Physics of the Earth RAS (Moscow)
c NPO Taifun, Russian Federal Survey for Hydro meteorology and Environmental Monitoring (Obninsk)

Abstract: Currently, there are a number of ways to determine trends and extremes in stochastic time series, which is not surprising, since time series trends are a fundamental characteristic of the dynamics of the process behind it.
Real stochastic trends are not at all like ideal mathematical ones, because they contain violations. This does not bother the researcher, who initially has an adaptive perception of the fundamental properties of extremeness, continuity, connectedness, trend, etc. He will understand when the violation is insignificant and the trend continues, and when the violation interrupts the trend.
In this paper, we propose a new approach to the recognition of stochastic trends, based on the mathematical construction of regression derivatives for a finite time series. Trends are sought using the derivative from the scenario of classical mathematical analysis.

Keywords: fuzzy mathematics, nearness measures, regression derivatives, trends.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation
The study was carried out within the framework of the state task of The geophysical center of the Russian Academy of Sciences, approved by the Ministry of education and science of Russia.


DOI: https://doi.org/10.22405/2226-8383-2018-20-3-92-106

Full text: PDF file (2575 kB)

UDC: 51-7, 519.816
Received: 08.10.2019
Accepted:12.11.2019

Citation: S. M. Agayan, Sh. R. Bogoutdinov, D. A. Kamaev, M. N. Dobrovolsky, “Stochastic trends based on fuzzy mathematics”, Chebyshevskii Sb., 20:3 (2019), 92–106

Citation in format AMSBIB
\Bibitem{AgaBogKam19}
\by S.~M.~Agayan, Sh.~R.~Bogoutdinov, D.~A.~Kamaev, M.~N.~Dobrovolsky
\paper Stochastic trends based on fuzzy mathematics
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 3
\pages 92--106
\mathnet{http://mi.mathnet.ru/cheb800}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-3-92-106}


Linking options:
  • http://mi.mathnet.ru/eng/cheb800
  • http://mi.mathnet.ru/eng/cheb/v20/i3/p92

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:6
    Full text:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020