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.


Download data is not yet available.

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.


Alizadeh M., M. T. H. Beheshti, A. Ramezani and H. Saadatinezhad. Network Traffic Forecasting Based on Fixed Telecommunication Data Using Deep Learning. In Proceedings of the 2020 6th Iranian Conference on Signal Processing and Intelligent Systems (ICSPIS), 2020. doi: 10.1109/ICSPIS51611.2020.9349573.

Balamurugan, N. M., M. Adimoolam, M. H. Alsharif and P. Uthansakul. A Novel Method for Improved Network Traffic Prediction Using Enhanced Deep Reinforcement Learning Algorithm. Sensors 22:5006, 2022. doi: 10.3390/s22135006.

Tian, Z. and F. Li. Network traffic prediction method based on autoregressive integrated moving average and adaptive Volterra filter. Int J Commun Syst. 34:e4891, 2021. doi: 10.1002/dac.4891.

Lv, T., Y. Wu and L. Zhang. A Traffic Interval Prediction Method Based on ARIMA. Journal of Physics: Conference Series 1880:012031, 2021. doi: 10.1088/1742-6596/1880/1/012031.

Kim, M. Network traffic prediction based on INGARCH model. Wireless Networks 26:6189–6202, 2020. doi: 10.1007/s11276-020-02431-y.

Ji, Y., D. Zhang, Y. Yuan, S. Liu, R. Zarei and J. He. A Novel Flash P2P Network Traffic Prediction Algorithm based on ELMD and Garch. International Journal of Information Technology & Decision Making 19:127, 2020. doi: 10.1142/S0219622019500469.

Lohrasbinasab, I., A. Shahraki, A. Taherkordi and A. D. Jurcut. From statistical- to machine learning-based network traffic prediction. Trans Emerging Tel Tech. 33:e4394, 2022. doi: 10.1002/ett.4394.

Chen, A., J. Law and M. Aibin. A Survey on Traffic Prediction Techniques Using Artificial Intelligence for Communication Networks. Telecom 2:518–535, 2021. doi.org/10.3390/telecom2040029.

Kashyap, A. A., S. Raviraj, A. Devarakonda, R. N. K. Shamanth, K. V. Santhosh and S. J. Bhat. Traffic flow prediction models – A review of deep learning techniques. Cogent Engineering, 9:1, 2010510, 2021. doi: 10.1080/23311916.2021.2010510.

Jiang, W. and J. Luo. Graph neural network for traffic forecasting: A survey. Expert Systems with Applications 207:117921, 2022. doi: 10.1016/j.eswa.2022.117921.

Shi, J., Y.-B. Leau, K. Li, J. H. Obit. A comprehensive review on hybrid network traffic prediction model. International Journal of Electrical and Computer Engineering (IJECE) 11:1450, 2021. doi: 10.11591/ijece.v11i2.pp1450-1459.

Li, Y., J. Huang and H. Chen. Time Series Prediction of Wireless Network Traffic Flow Based on Wavelet Analysis and BP Neural Network. Journal of Physics: Conference Series 1533:032098, 2020. doi: 10.1088/1742-6596/1533/3/032098.

Hajirahimi Z., M. Khashei. Hybrid structures in time series modeling and forecasting: A review. Engineering Applications of Artificial Intelligence 86:83–106, 2019. doi: 10.1016/j.engappai.2019.08.018.

Saganowski, L. and T. Andrysiak. Time series forecasting with model selection applied to anomaly detection in network traffic. Logic Journal of the IGPL 28:531–545, 2020. doi: 10.1093/jigpal/jzz059.

Liu, F., Q. Li and Y. Liu. Network Traffic Big Data Prediction Model Based On Combinatorial Learning. In Proceedings of 2019 IEEE Fifth International Conference on Big Data Computing Service and Applications (BigDataService), 2019. doi: 10.1109/BigDataService.2019.00044.

Tian, Z. Network traffic prediction method based on wavelet transform and multiple models fusion. Int J Commun Syst., e4415, 2020. doi: 10.1002/dac.4415.

Li, Y., Z. Ma, Z. Pan, N. Liu and X. You. Prophet model and Gaussian process regression based user traffic prediction in wireless networks. Sci. China Inf. Sci. 63:142301, 2020. doi: 10.1007/s11432-019-2695-6.

Li, M. Generalized fractional Gaussian noise and its application to traffic modeling. Physica A, 579:126138, 2021. doi: 10.1016/j.physa.2021.12613.

Da Silva, M. R. P., and F. G. C. Rocha. Traffic modeling for communications networks: A multifractal approach based on few parameters. Journal of the Franklin Institute 358:2161–2177, 2021. doi: 10.1016/j.jfranklin.2020.12.015.

Gorev V., A. Gusev, V. Korniienko and M. Aleksieiev, Kolmogorov–Wiener Filter Weight Function for Stationary Traffic Forecasting: Polynomial and Trigonometric Solutions. In P. Vorobiyenko, M. Ilchenko, I. Strelkovska (Eds.), Lecture Notes in Networks and Systems, Springer, 212:111–129, 2021. doi: 10.1007/978-3-030-76343-5_7.

Li, M. Fractal Teletraffic Modeling and Delay Bounds in Computer Communications, CRC Press, Boca Raton, 2022. doi: 10.1201/9781003268802.

Diniz, P. S. R. Adaptive Filtering Algorithms and Practical Implementation, 5th ed., Springer Nature Switzerland AG, Cham, 2020. doi: 10.1007/978-3-030-29057-3.

Dogariu, L.-M., J. Benesty, C. Paleologu and S. Ciochin. An Insightful Overview of the Wiener Filter for System Identification. Appl. Sci., 11: 7774, 2021. doi: 10.3390/app11177774.

Pollock, D. S. G. Enhanced Methods of Seasonal Adjustment. Econometrics, 9:3, 2021. doi: 10.3390/econometrics9010003.

Alwazzan, M. J., M. A. Ismael and A. N. Ahmed. A Hybrid Algorithm to Enhance Colour Retinal Fundus Images Using a Wiener Filter and CLAHE. Journal of Digital Imaging 34:750–759, 2021. doi: 10.1007/s10278-021-00447-0.

Wu, Y.-W., S. Li, Y. Liu, H. Liu and H. Li. Study on the filters of atmospheric contamination in ground based CMB observation. arXiv preprint, arXiv:2210.09711, 10 2022.

Malaguti, G., P. R. ten Wolde. Theory for the optimal detection of time-varying signals in cellular sensing systems. eLife 10:e62574, 2021. doi: 10.7554/eLife.62574.

Celenk, M., T. Conley, J. Graham and John Willis. Anomaly Prediction in Network Traffic Using Adaptive Wiener Filtering and ARMA Modeling. In Proceedings of the 2008 IEEE International Conference on Systems, Man and Cybernetics (SMC 2008), 2008. doi: 10.1109/ICSMC.2008.4811848.

Ahrens, A., C. Lange and C. Benavente-Peces. Traffic Estimation for Dynamic Capacity Adaptation in Load Adaptive Network Operation Regimes. In Proceedings of the 6th International Joint Conference on Pervasive and Embedded Computing and Communication Systems (PECCS 2016), 2016. doi: 10.5220/0005932800990104.

Barreto, S. M. P. A., M. J. P. Dantas, R. P. Lemos. ATM Traffic Prediction Methods Using Wavelet Analysis. In Proceedings of the 2nd Latin American Network Operations and Management Symposium, LANOMS 2001, 2001. Available at: http://www.lanoms.org/2005/anaiscd/2001/5-3.pdf.

Gorev, V., A. Gusev and V. Korniienko. The use of the Kolmogorov–Wiener filter for prediction of heavy-tail stationary processes. CEUR Workshop Proceedings, 3156:150–159, 2022. Available at: http://ceur-ws.org/Vol-3156/paper9.pdf.

Gorev, V., A. Gusev and V. Korniienko. Fractional Gaussian Noise Traffic Prediction Based on the Walsh Functions. CEUR Workshop Proceedings, 2853:389–400, 2021. Available at: http://ceur-ws.org/Vol-2853/paper35.pdf.

Gorev, V. N., A. Yu. Gusev, V. I. Korniienko and A. A. Safarov. On the Kolmogorov-Wiener filter for random processes with a power-law structure function based on the Walsh functions. Radio Electronics, Computer Science, Control, 2:39–47, 2021. doi: 10.15588/1607-3274-2021-2-4.

Gorev, V. N., A. Yu. Gusev and V. I. Korniienko. On the Kolmogorov-Wiener filter for continuous traffic prediction in the GFSD model. Radio Electronics, Computer Science, Control, 3:31–37, 2022. doi: 10.15588/1607-3274-2022-3-3.

Papaika, Yu. A., O. H. Lysenko, Ye. V. Koshelenko and I. H. Olishevskyi. Mathematical modeling of power supply reliability at low voltage quality. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, 2:97–103, 2021. doi: 10.33271/nvngu/2021-2/097.




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 Dec. 4];12(03):315–338. Available from: https://journals.riverpublishers.com/index.php/JCSANDM/article/view/18785



Assurance of Information Systems’ Quality and Security