Avrupa Ülkererinin Haberleşme Sektöründeki Yatırımlarının Matematiksel Modellenmesi

Abstract

Bu çalışma, ülkelerin telekomünikasyon yatırımlarının miktarlarını araştırmakta ve verileri matematiksel olarak modellemek için uygun bir yöntem aramaktadır. Çalışmada kesirli kalkülüs kullanılarak model 1 ve model 2 olarak adlandırılan iki yöntem önerilmiştir. Fransa, Almanya, İtalya, İspanya, Türkiye ve OECD toplamından elde edilen telekomünikasyon yatırımlarının yıllık verileri kullanılarak geleneksel polinom modeli ile 1 ve 2 modelleri arasında bir karşılaştırma yapılmıştır. Önerilen yöntemler, geleneksel polinom modelinden daha iyi performans gösterdiği gözlenmiştir.

Keywords

• haberleşme sektöründeki yatırımlar
• kesirli türev
• MAPE
• haberleşme sektöründeki yatırımlar, kesirli türev, MAPE

Mathematical Modeling of European Countries’ Telecommunication Investments

Abstract

This study investigates the amounts of countries’ telecommunication investments and seeks a decent method to mathematically model the data. Using fractional calculus, two methods are proposed which are called model 1 and model 2 in the study. A comparison is performed between the conventional polynomial model and models 1 and 2 using the yearly data of telecommunication investments from France, Germany, Italy, Spain, Turkey, and the OECD total. The proposed methods outperform the conventional polynomial model.

Keywords

• Fractional calculus
• MAPE
• modeling; telecommunications investments

References

1. [1]. Aytun C., Akın C. S., and Okyay U., Relationship between telecommunication investments and foreign direct investments in developing and developed countries, Ege Acad. Rev., 2015, 15(2), 207–216.
2. [2]. Beil R. O., Ford G. S., and Jackson J. D., On the relationship between telecommunications investment and economic growth in the United States, Int. Econ. J., 2005, 19(1), 3–9.
3. [3]. Kotakorpi K., Access price regulation, investment and entry in telecommunications, Int. J. Ind. Organ., 2006, 24(5), 1013–1020.
4. [4]. Önal N. Ö., Karaçuha K., Erdinç G. H., Karaçuha B. B., and Karaçuha E., A mathematical approach with fractional calculus for the modelling of children’s physical development, Comput. Math. Methods Med., 2019, 2019.
5. [5]. Machado J. T., Kiryakova V., and Mainardi F., Recent history of fractional calculus, Commun. nonlinear Sci. Numer. Simul., 2011, 16(3), 1140–1153.
6. [6]. Key ict indicators, OECD. [Online]. Available: https://www.oecd.org/digital/broadband/oecdkeyictindicators.htm. [Accessed: 15-Sep-2021].
7. [7]. Doh J. P. and Teegen H. J., Private telecommunications investment in emerging economies: Comparing the Latin American and Asian experience, Manag. Res. J. Iberoam. Acad. Manag., 2003.
8. [8]. Royston P. and Altman D. G., Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling, J. R. Stat. Soc. Ser. C Applied Stat., 1994, 43(3), 429–453.

9. [9]. Podlubny I., Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, 1998.
10. [10]. Loverro A., Fractional calculus: history, definitions and applications for the engineer, Rapp. Tech. Univeristy Notre Dame Dep. Aerosp. Mech. Eng., 2004, 1–28,.
11. [11]. Chang H., Koski H., and Majumdar S. K., Regulation and investment behaviour in the telecommunications sector: Policies and patterns in US and Europe, Telecomm. Policy, 2003, 27(10–11), 677–699.
12. [12]. Henisz W. J. and Zelner B. A., The institutional environment for telecommunications investment, J. Econ. Manag. Strateg., 2001, 10(1), 123–147.
13. [13]. Madden G. and Savage S. J., CEE telecommunications investment and economic growth, Inf. Econ. Policy, 1998, 10(2), 173–195.
14. [14]. Roller L. H. and Waverman L., Telecommunications infrastructure and economic development: A simultaneous approach, Am. Econ. Rev., 2001, 91(4), 909–923.
15. [15]. Karaçuha K., Tabatadze V., and Veliev E. I., Plane wave diffraction by strip with an integral boundary condition, Turkish J. Electr. Eng. Comput. Sci., 2020, 28(3), 1776–1790.
16. [16]. Karaçuha E. et al., Modeling and Prediction of the Covid-19 Cases With Deep Assessment Methodology and Fractional Calculus, IEEE Access, 2020, 8, 164012–164034.
17. [17]. E. Karaçuha, V. Tabatadze, K. Karaçuha, N. Ö. Önal, and E. Ergün, Deep Assessment Methodology Using Fractional Calculus on Mathematical Modeling and Prediction of Gross Domestic Product per Capita of Countries, Mathematics, 2020, 8(4), 633.
18. [18]. Önal, N. Ö., Karacuha, K., and Karacuha, E., A Comparison of Fractional and Polynomial Models: Modelling on Number of Subscribers in the Turkish Mobile Telecommunications Market, Int. J. Appl. Phys. Math., 2019, 10.
19. [19]. Önal, N. Ö., Karacuha, K., & Karacuha, E., Modelling on Economic Growth and Telecommunication Sector of Turkey Using a Fractional Approach Including Error Minimizing, in 3rd Asia-Pacific Conference on Applied Mathematics and Statistics (AMS 2020), Feb. 2020.