Оценка параметров инфокоммуникационной сети методом наименьших квадратов

A A Sherstneva

doi:10.22213/2413-1172-2021-2-85-91

Authors

A. A. Sherstneva Siberian State University of Telecommunications and Information Sciences

DOI:

https://doi.org/10.22213/2413-1172-2021-2-85-91

Keywords:

regression, least squares estimation, data trend, exponential function, power function

Abstract

The paper purposes for predicting data trend for calculating infocommunication system’s parameters. As a result, a solution to the problem of determining the changing values of time series is proposed, assuming that it has a linear relationship with another time series in the models of infocommunication systems. Regression analysis is used to determine parameters values from a set of observational data. The paper deals with power and exponential regression. Mathematical modeling programs developed for multiple regression models can be used to test the adequacy of autoregressive models on the basis that the least-squares estimation problems of multiple linear regression parameters do not have significant differences with p-order autoregression. In this case, partial correlations between components of the series with more than five steps apart from each other are equal to zero. The considered methodology is of interest because modern infocommunication systems are complex systems with many states and co-dependencies between them. Therefore, the task of short-term forecasting simulation simplifies the process of finding the parameters. The software implementation of the solution was worked out in Matlab. An experimental method was used to obtain a least squares estimation of the theoretical parameters of models. The generated experimental data are shown for each model with corresponding exponential and power regression curves. The results of software modeling confirm the use of LSE approach. During the software implementation, the predicted values of the incoming call flow to the system were simulated.

Author Biography

A. A. Sherstneva, Siberian State University of Telecommunications and Information Sciences

PhD in Engineering

References

Степанов С. Н. Теория телетрафика: концепции, модели, приложения. М. : Горячая линия - Телеком, 2015, 868 с.

Домбровский В. В., Объедко Т. Ю. Оптимальные стратегии прогнозирующего управления системами со случайными параметрами, описываемыми многомерной регрессионной моделью с марковским переключением режимов // Вестник Томского гос. ун-та, УВТиИ. 2019. № 48. С. 4-12.

Домбровский В. В., Пашинская Т. Ю. Прогнозирующее управление системами с марковскими скачками и авторегрессионным мультипликативным шумом с марковским переключением режимов // Вестник Томского гос. ун-та, УВТиИ. 2018. № 44. С. 4-9.

Bergmeir C., Hyndman R.J., Benítez J.M. Bagging exponential smoothing methods using STL decomposition and Box-Cox transformation. International J. of Forecasting, 2016, 32, pp. 303-312.

Hyndman R.J., Athanasopoulos G. Forecasting: principles and practice. OTexts: Melbourne, Australia, 2d edition, 2018, 378 p.

Ord J.K., Fildes R., Kourentzes N. Principles of business forecasting. Wessex Press Publishing Co, 2017, 865 p.

Bergmeir C., Hyndman R.J., Koo B. A note on the validity of cross-validation for evaluating autoregressive time series prediction. Computational Statistics and Data Analysis, 2018, 120, pp. 70-83.

Wickramasuriya S.L., Athanasopoulos G. Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. J. American Statistical Association, 2019, no. 114, pp. 804-819.

Nielsen A. Practical time series analysis. New York, USA, O’Reilly media, 2020, 470 p.

Сток Д., Уотсон М. Введение в эконометрику. М. : Дело, 2019. 835 p.

Кирин Р. В., Канторович Г. Г. Применение EM-алгоритма для поиска структурных сдвигов во временных рядах // Труды 11-й Междунар. науч.-практ. конф. студентов и аспирантов. М. : Высшая школа экономики, 2020, с. 90-92.

Racine J.S. Reproducible econometrics using R. NY, Oxford University Press, 2019, 293 p.

Bergmeir P. Enhanced machine learning and data mining methods for analysing large hybrid electric vehicle fleets based on load spectrum data. Springer, Germany, 2019, 167 p.

Theodoridis S. Machine learning: A Bayesian and optimization perspective. Elsevier, Academic Press, 2020, 1160 p.

Farebrother R.W. Linear least squares computations. CRC Press, USA, 2018, 320 p.

Özbay N., Kaçıranlar S. Estimation in a Linear Regression Model with Stochastic Linear Restrictions: a New Two-parameter-weighted Mixed Estimator. Taylor & Francis, 2018, 322 p.

Therrien C., Tummala M. Probability and Random Processes for Electrical and Computer Engineers. CRC Press, USA, 2018, 431 p.