Stochastic trends based on fuzzy mathematics
https://doi.org/10.22405/2226-8383-2019-20-3-92-106
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.
Supporting agencies: 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
About the Authors
Sergey Martikovich Agayan
Геофизический центр РАН (г. Москва)
Russian Federation
Russian Federation
doctor of physical and mathematical Sciences, Principal research scientist, Geophysical Center RAS (Moscow)
Shamil Rafekovich Bogoutdinov
Russian Federation
candidate of physical and mathematical Sciences, Leading research scientist, Geophysical Center RAS; Senior research scientist, Schmidt Institute of Physics of the Earth RAS (Moscow)
Dmitry Alfredovich Kamaev
Russian Federation
doctor of engineering, Chief of laboratory, NPO «Taifun», Russian Federal Survey for Hydro meteorology and Environmental Monitoring (Obninsk).
Mikhail Nikolaevich Dobrovolsky
Russian Federation
candidate of physical and mathematical Sciences, Senior research scientist, Geophysical Center RAS (Moscow)
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Review
For citations:
Agayan S.M., Bogoutdinov Sh.R., Kamaev D.A., Dobrovolsky M.N. Stochastic trends based on fuzzy mathematics. Chebyshevskii Sbornik. 2019;20(3):92-106. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-3-92-106
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