On the Use of the Kolmogorov–Wiener Filter for Heavy-tail Process Prediction


  • Vyacheslav Gorev Dnipro University of Technology, Dnipro, Ukraine
  • Alexander Gusev Dnipro University of Technology, Dnipro, Ukraine
  • Valerii Korniienko Dnipro University of Technology, Dnipro, Ukraine
  • Yana Shedlovska Dnipro University of Technology, Dnipro, Ukraine




Discrete Kolmogorov–Wiener filter, continuous Kolmogorov–Wiener filter, heavy-tail process, telecommunication traffic prediction


This paper is devoted to the investigation of the applicability of the Kolmogorov–Wiener filter to the prediction of heavy-tail processes. As is known, telecommunication traffic in systems with data packet transfer is considered to be a heavy-tail process. There are a lot of rather sophisticated approaches to traffic prediction; however, in the rather simple case of stationary traffic sophisticated approaches may not be needed, and a simple approach, such as the Kolmogorov–Wiener filter, may be applied. However, as far as we know, this approach has not been considered in recent papers. In our previous papers, we theoretically developed a method for obtaining the filter weight function in the continuous case. The Kolmogorov–Wiener filter may be applied only to stationary processes, but in some models telecommunication traffic is treated as a stationary process, and thus the use of the Kolmogorov–Wiener filter may be of practical interest. In this paper, we generate stationary heavy-tail modeled data similar to fractional Gaussian noise and investigate the applicability of the Kolmogorov–Wiener filter to data prediction. Both non-smoothed and smoothed processes are investigated. It is shown that both the discrete and the continuous Kolmogorov–Wiener filter may be used in a rather accurate short-term prediction of a heavy-tail smoothed stationary random process. The paper results may be used for stationary telecommunication traffic prediction in systems with packet data transfer.


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Author Biographies

Vyacheslav Gorev, Dnipro University of Technology, Dnipro, Ukraine

Vyacheslav Gorev in 2012 graduated from the Department of Theoretical Physics of Oles Honchar Dnipro National University. In 2016 received the Ph.D. degree in theoretical physics. From 2017 to 2023 worked at the Department of Information Security and Telecommunications of Dnipro University of Technology; since 2023 has been working as the head of the Department of Physics, Dnipro University of Technology.

Alexander Gusev, Dnipro University of Technology, Dnipro, Ukraine

Alexander Gusev graduated from the Department of Automation and Telemechanics, Novosibirsk Electrotechnical Institute, in 1972. From 1972 to 1983 worked in the Siberian Branch of the USSR Academy of Sciences. In 1982 received the Ph.D. degree. From 1983 to 2005 worked at the Dnepropetrovsk Research Institute of Automation. Since 2005 has been working as an Associate Professor and Professor at Dnipro University of Technology.

Valerii Korniienko, Dnipro University of Technology, Dnipro, Ukraine

Valerii Korniienko graduated from Dnipropetrovsk Mining Institute in the specialty ‘Automation and Telemechanics’ in 1979. Since 2016 he has been Head of the Department of Information Security and Telecommunications, Dnipro University of Technology. He has 130 scientific publications. His inventions were used in the Ocean-O Ukrainian-Russian space vehicle. Doctor of Engineering Science (2010), Professor (2011).

Yana Shedlovska, Dnipro University of Technology, Dnipro, Ukraine

Yana Shedlovska graduated from the National Mining University (Dnipro, Ukraine) in 2012. In 2021 received the Ph.D. degree in applied geometry and engineering graphics. Since 2021 has been working at the Department of Information Technology and Computer Engineering, Dnipro University of Technology.


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How to Cite

Gorev V, Gusev A, Korniienko V, Shedlovska Y. On the Use of the Kolmogorov–Wiener Filter for Heavy-tail Process Prediction. JCSANDM [Internet]. 2023 May 18 [cited 2023 May 31];12(03):315–338. Available from: https://journals.riverpublishers.com/index.php/JCSANDM/article/view/18785



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