Matrixes least squares method: examples of its application in macroeconomics and TV-media business

Authors

  • Volodymyr Donchenko Taras Shevchenko National University of Kyiv str. Vladimirskaja, 60, Kiev, 01601, Ukraine
  • Inna Nazaraga Taras Shevchenko National University of Kyiv str. Vladimirskaja, 60, Kiev, 01601, Ukraine
  • Olga Tarasova Taras Shevchenko National University of Kyiv str. Vladimirskaja, 60, Kiev, 01601, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2014.26292

Keywords:

Moore-Penrose pseudo inverse, regression, least squares method, macroeconomic, prediction, econometrics

Abstract

In the paper general framework of Least Square Method (LSM) on vectors and matrixes observation is represented. Also the results developing M-Ppi technique are submitted. Some principal examples are represented in the article. These examples illustrate the advantages of LSM in the case under consideration. General algorithm LSM with matrixes observations is proposed and described in step-by-step variant for linear and nonlinear scaled data. The examples of method applications in macroeconomics and TV-media business illustrate the advantages and capabilities of the method. Correspondent results are also represented below as well as illustration of its applications for predicting in macroeconomics of Ukraine and in estimating of TV audience. The proposed approach for finding predictive values indicators is competitive.

Author Biographies

Volodymyr Donchenko, Taras Shevchenko National University of Kyiv str. Vladimirskaja, 60, Kiev, 01601

Professor

Department of system analysis and decision making theory

Inna Nazaraga, Taras Shevchenko National University of Kyiv str. Vladimirskaja, 60, Kiev, 01601

Ph.D. (Tech.)

Department of system analysis and decision making theory

Olga Tarasova, Taras Shevchenko National University of Kyiv str. Vladimirskaja, 60, Kiev, 01601

Ph.D.-student

Department of system analysis and decision making theory

References

  1. Magnus, Y. R., Katyshev, P. K., Peresetskij, A. A. (2007). Ekonometrika. Nachalnyi kurs. Moscow: Delo, 504.
  2. Seraya, O. V., Demin, D. A. (2012). Linear Regression Analysis of a Small Sample of Fuzzy Input Data. J Automat Inf Scien, 44 (7), 34–48. doi:10.1615/jautomatinfscien.v44.i7.40
  3. Seraya, O. V., Demin, D. A. (2010). Estimation of representative truncated orthogonal subplans of complete factor experiment plan. System Research and Information Technologies, 3, 84–88.
  4. Demin, D. A. (2013). Artificial orthogonalization in searching of optimal control of technological processes under uncertainty conditions. Eastern-European journal of enterprise technologies, 5/9 (65), 45-53. – Mode of access : WWW/ URL: http://journals.uran.ua/eejet/article/view/18452/ — 31.07.2014. — Title from the screen.
  5. Nazaraga, I. M. (2010). Povedinkova model ta model portfelia aktyviv vyznachennia obminnogo kursu v umovah ekonomiky Ukrainy. Matematychne ta kompiuterne modeliuvannia, 3, 160–168.
  6. Kharazishvili, Yu. M., Nazaraga, I. M. (2012). Investitsii: pidhid do prognozuvannia. Actual problems of economics, 9 (135), 213–222.
  7. Slutskin, L. N. (2006). Kurs MBA po prognozirovaniiu v biznese. Moskow: Alpina Biznes Buk, 280.
  8. Donchenko, V. S., Nazaraga, I. M., Tarasova, O. V. (2013). Vectors and matrixes least square method: foundation and application examples. International Journal “Information Theories & Applications”, 20 (4), 311–322.
  9. Moore, E. H. (1920). On the reciprocal of the general algebraic matrix. Bulletin of the American Mathematical Society, 26, 394–395.
  10. Penrose, R. (1955). A generalized inverse for matrices. Proceedings of the Cambridge Philosophical Society, 51, 406–413.
  11. Kyrychenko, M. F., Donchenko, V. S. (2005). Zadacha terminalnoho sposterezhennia dynamichnoi systemy: mnozhynnist rozviazkiv ta optymizatsiia. Journal of Numerical and Applied Mathematics, 5, 63–78.
  12. Albert, A. (1977). Regression and the Moore-Penrose pseudoinverce. Moscow, USSR: Nauka, 305.
  13. Donchenko, V. (2011). Evklidovy prostranstva chislovykh vektorov I matrits: konstruktivnye metody opisaniia bazovykh struktur i ikh ispolzovanie. International Journal “Information technologies & Knowledge”, 5 (3), 203–216.
  14. Donchenko, V., Krivonos, Yu., Krak, Yu. (2012). Recurrent procedure in solving the grouping information problem in applied mathematics. International Journal “Information Models and Analyses”, 1, 62–77.
  15. Donchenko, V. (2013). Matrixes least squares method and examples of its application. International Journal “Information Technologies & Knowledge”, 7 (4), 325-336.
  16. Official web-site of the Ministry of Economic Development and Trade of Ukraine. The Ministry of Economic Development and Trade of Ukraine. Available at : http://www.me.gov.ua/. Last accessed 30.03.2014.
  17. Official web-site of the State Statistics Service of Ukraine. The State Statistics Service of Ukraine. Available at : http://www.ukrstat.gov.ua/. Last accessed 30.03.2014.
  18. Swann, P., Tavakoli, M. (1994). An econometric analysis of television viewing and the welfare economics of introducing an additional channel in the UK. Information Economics and Policy, 6 (1), 25–51. doi:10.1016/0167-6245(94)90035-3
  19. Official site of GfK Ukraine Media. GfK Ukraine Media. Available at : http://www.gfk.ua/. Last accessed 31.12.2013.

Downloads

Published

2014-07-24

How to Cite

Donchenko, V., Nazaraga, I., & Tarasova, O. (2014). Matrixes least squares method: examples of its application in macroeconomics and TV-media business. Eastern-European Journal of Enterprise Technologies, 4(4(70), 42–46. https://doi.org/10.15587/1729-4061.2014.26292

Issue

Vol. 4 No. 4(70) (2014): Mathematics and cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2014 Volodymyr Donchenko, Inna Nazaraga, Olga Tarasova

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.