Forecasting the Population of Türkiye Using Grey Models

Abstract

Population forecasting plays a significant role in determining demography, economics, and agriculture policies for developing countries. In this study, we employ the five different grey prediction models to estimate the population of Türkiye until 2050 using the 2007 to 2022 address-based data. These models are given as the grey standard (GM (1,1)), grey time-varying dynamic (GM (1,1) t), grey Gompertz (GGM), grey Verhulst (GVM), and grey exponential (EXGM (1,1). The comparison of grey models is evaluated by mean absolute percentage error (MAPE), regression coefficient (R2), variance ratio (C), and probability of error (P). The GGM and GM (1,1) t are identified as the most suitable models for predicting the period 2007-2022. For the future population forecasts from 2023 to 2050, the five models are compared with the projection values of the Turkish Statistical Institute published in 2018. The GGM is determined to be the most compatible based on the MAPE value of 0.68116 and the C value of 0.05218, and the Grey Verhulst model is provided the most compatible R2 value of 0.99818. According to the GGM, the population of Türkiye is projected to reach 105,948,975 by 2050, 106,877,632 based on the GM (1,1) t, and 102,591,471 based on the GVM.

Keywords

• Population Forecasting
• Grey System
• Grey Prediction
• GM (1,1)
• Time Series

References

1. Akay, D., & Atak, M. (2007). Grey prediction with rolling mechanism for electricity demand forecasting of Turkey. Energy, 32(9), 1670–1675. https://doi.org/10.1016/j.energy.2006.11.014
2. Aksu, L. (1998). Dünya'da ve Türkiye'de Nüfus Analizleri. Istanbul Journal of Sociological Studies, 25, 219–311.
3. Akyuz, L. (2002). Zaman Serilerinin Tahmini İçin Gri Modelleme Metodu.
4. Akyüz, L., & Bilgil, H. (2022). GM (1,1) ve EXGM (1,1) Tahmin Modellerinin Türkiye'nin Ar-Ge Harcamalarına Uygulanması. Aksaray University Journal of Science and Engineering, 6(2), 95–106. https://doi.org/10.29002/asujse.1087288
5. Aydemir, E., & Sahin, Y. (2019). Evaluation of healthcare service quality factors using grey relational analysis in a dialysis center. Grey Systems: Theory and Application, 9(4), 432–448. https://doi.org/10.1108/gs-01-2019-0001
6. Aydemir, E., Bedir, F., & Özdemir, G. (2013). Gri Sistem Teorisi ve Uygulamaları: Bilimsel Yazın Taraması. Süleyman Demirel Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi, 18(3), 187–200.
7. Ayhan Selçuk, İ. (2014). Extrapolation Population Projection Method as Being a Tool for the Bias of Short-term Needs of Urban Social and Technical Infrastructure: the Case of Kutahya. International Refereed Journal of Design and Architecture, 1(2), 98. https://doi.org/10.17365/TMD.201429190
8. Başakın, E. E., Özger, M., & Ünal, N. E. (2019). Gri Tahmin Yöntemi İle İstanbul Su Tüketiminin Modellenmesi. Politeknik Dergisi, 22(3), 755–761. https://doi.org/10.2339/politeknik.422727

9. Bilgil, H. (2021). New grey forecasting model with its application and computer code. AIMS Mathematics, 6(2), 1497–1514. https://doi.org/10.3934/math.2021091
10. Cai, K., & Wu, L. (2022). Using grey Gompertz model to explore the carbon emission and its peak in 16 provinces of China. Energy and Buildings, 277, 112545. https://doi.org/10.1016/j.enbuild.2022.112545
11. Deng, J. L. (1982). Control problems of grey systems. Systems & Control Letters, 1(5), 288–294. https://doi.org/10.1016/s0167-6911(82)80025-x
12. Deng, J. L. (1989). Introduction to Grey System Theory. The Journal of Grey System, 1(1), 1–24.
13. Ding, S., Dang, Y., Xu, N., Chen, D., & Cui, J. (2015). The Optimization of Grey Verhulst Model and Its Application. The Journal of Grey System, 27(2), 1–13.
14. Ding, Y., & Dang, Y. (2023). Forecasting renewable energy generation with a novel flexible nonlinear multivariable discrete grey prediction model. Energy, 277, 127664. https://doi.org/10.1016/j.energy.2023.127664
15. Duan, H., & Luo, X. (2020). Grey optimization Verhulst model and its application in forecasting coal-related CO2 emissions. Environmental Science and Pollution Research, 27(35), 43884–43905. https://doi.org/10.1007/s11356-020-09572-9
16. Erdinc, U., Bilgil, H., & Ozturk, Z. (2024). Novel Fractional Forecasting Model for Time Dependent Real World Cases. REVSTAT-Statistical Journal, 169–188. https://doi.org/10.57805/REVSTAT.V22I2.468
17. Eren, T., & Kaçtıoğlu, S. (2017). Türkiye'deki Doğal Gaz Tüketimi Ve Gri Tahmin Metoduyla Tahmin Edilmesi. İstanbul Commerce University Journal of Science, 16(31), 23–41.
18. Evans, M. (2014). An alternative approach to estimating the parameters of a generalised Grey Verhulst model: An application to steel intensity of use in the UK. Expert Systems with Applications, 41(4), 1236–1244. https://doi.org/10.1016/j.eswa.2013.08.006
19. Fendoğlu, E. (2021). Population Forecast With the Data Processing Group Method (GMDH) Type Neural Network for European Union Countries. IEDSR Association, 6(15), 563–598. https://doi.org/10.46872/pj.323
20. Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of Life Contingencies. Philosophical Transactions of the Royal Society of London, 115, 513–583. https://doi.org/10.1098/rstl.1825.0026
21. Güzel, Ş. (2018). Tarihi Coğrafya Yönüyle, 1841 Tarihli Nüfus Defterine Göre Burdur Şehri ve Çevresinin Nüfusu.
22. Hopkins, W. G. (2002, ). A Scale of Magnitudes for Effect Statistics. https://www.sportsci.org/resource/stats/effectmag.html
23. Hsu, C.-I., & Wen, Y.-H. (1998). Improved grey prediction models for the trans-pacific air passenger market. Transportation Planning and Technology, 22(2), 87–107. https://doi.org/10.1080/03081069808717622
24. İskender, C. (2018). Türkiye Nüfus Büyümesi ve Tahminleri: Matematiksel Büyüme Modelleri ve İstatistiksel Analiz İle Kuramsal ve Uygulamalı Bir Yaklaşım. EKOIST Journal of Econometrics and Statistics, 14(28), 75–141. https://doi.org/10.26650/ekoist.2018.14.2
25. Javanmardi, E., Liu, S., & Xie, N. (2023). Exploring the Challenges to Sustainable Development from the Perspective of Grey Systems Theory. Systems, 11(2), 70. https://doi.org/10.3390/systems11020070
26. Kayacan, E., Ulutas, B., & Kaynak, O. (2010). Grey system theory-based models in time series prediction. Expert Systems with Applications, 37(2), 1784–1789. https://doi.org/10.1016/j.eswa.2009.07.064
27. Köse, M., & Sertkaya Doğan, Ö. (2022). Nüfus Politikaları Bağlamında Türkiye Nüfusunun Demografik Dönüşümü, Yapısal Değişimi ve Geleceği. Dumlupınar Üniversitesi Sosyal Bilimler Dergisi, 74, 247–267. https://doi.org/10.51290/dpusbe.1152311
28. Küçükerdem Öztürk, T. S., & Saplıoğlu, K. (2023). Bursa İli Nüfusunun Gri Modelleme İle Tahmin Edilmesi. Çukurova 11th International Scientific Researches Conference, 479–488.
29. Lewis, C. D. (1982). Industrial and Business Forecasting Methods: A Practical Guide to Exponential Smoothing and Curve Fitting. Butterworths Publishing.
30. Liu, C., Wu, W.-Z., Xie, W., & Zhang, J. (2020). Application of a novel fractional grey prediction model with time power term to predict the electricity consumption of India and China. Chaos, Solitons & Fractals, 141, 110429. https://doi.org/10.1016/j.chaos.2020.110429
31. Liu, S., & Lin, Y. (2006). Springer-Verlag. https://doi.org/10.1007/1-84628-342-6
32. Liu, S., Yang, Y., & Forrest, J. (2017). Grey Data Analysis. Springer Singapore. https://doi.org/10.1007/978-981-10-1841-1
33. Liu, Z., Wang, M., & Wu, L. (2022). Countermeasures of Double Carbon Targets in Beijing–Tianjin–Hebei Region by Using Grey Model. Axioms, 11(5), 215. https://doi.org/10.3390/axioms11050215
34. Mostafaei, H., & Kordnoori, S. (2012). Hybrid Grey Forecasting Model for Iran's Energy Consumption and Supply. International Journal of Energy Economics and Policy, 2(3), 97–102.
35. Rathnayaka, R. K. T., & Seneviratna, D. (2024). Predicting of aging population density by a hybrid grey exponential smoothing model (HGESM): a case study from Sri Lanka. Grey Systems: Theory and Application, 14(3), 601–617. https://doi.org/10.1108/gs-01-2024-0002
36. Rayer, S., Smith, S. K., & Tayman, J. (2009). Empirical Prediction Intervals for County Population Forecasts. Population Research and Policy Review, 28(6), 773–793. https://doi.org/10.1007/s11113-009-9128-7
37. Riiman, V., Wilson, A., Milewicz, R., & Pirkelbauer, P. (2019). Comparing Artificial Neural Network and Cohort-Component Models for Population Forecasts. Population Review, 58(2). https://doi.org/10.1353/prv.2019.0008
38. Smith, S. K., & Sincich, T. (1992). Evaluating the forecast accuracy and bias of alternative population projections for states. International Journal of Forecasting, 8(3), 495–508. https://doi.org/10.1016/0169-2070(92)90060-m
39. Stoto, M. A. (1983). The Accuracy of Population Projections. Journal of the American Statistical Association, 78(381), 13–20. https://doi.org/10.1080/01621459.1983.10477916
40. TUIK. (2018). Nüfus Projeksiyonları, 2018-2080 (Issue 30567). https://data.tuik.gov.tr/Bulten/Index?p=Nufus-Projeksiyonlari2018-2080-30567
41. TUIK. (2023). Cinsiyete Göre Nüfus. Türkiye İstatistik Kurumu. https://nip.tuik.gov.tr/
42. Verhulst, P.-F. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondence Mathematique Et Physique, 10, 113–129.
43. Verhulst, P.-F. (1845). Recherches mathématiques sur la loi d'accroissement de la population. Nouveaux Mémoires De L'académie Royale Des Sciences Et Belles-Lettres De Bruxelles, 18(1), 1–40. https://doi.org/10.3406/marb.1845.3438
44. Verhulst, P.-F. (1847). Sur la loi d'accroissement de la population (Deuxième mémoire). Mémoires De L'académie Royale Des Sciences, Des Lettres Et Des Beaux-Arts De Belgique, 20(1), 1–32. https://doi.org/10.3406/marb.1847.3457
45. Wang, Z. L. (1998). Modeling Technique and Theory of Grey System.
46. Wang, Z. L. (2002). Abnormal GM(1,1): GM(1,1)t. The Journal of Grey System, 14(4), 371–374.
47. Wang, Z.-X., Li, D.-D., & Zheng, H.-H. (2020). Model comparison of GM(1,1) and DGM(1,1) based on Monte-Carlo simulation. Physica A: Statistical Mechanics and Its Applications, 542, 123341. https://doi.org/10.1016/j.physa.2019.123341
48. Wang, Z., Dang, Y., & Wang, Y. (2007). A new grey Verhulst model and its application. 2007 IEEE International Conference on Grey Systems and Intelligent Services, 571–574. https://doi.org/10.1109/gsis.2007.4443339
49. Wang, Z., Wang, Z., & Wei, T. (2008). Grey trend models. 2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 1841–1844. https://doi.org/10.1109/FUZZY.2008.4630620
50. Wen, K.-L., & Huang, Y.-F. (2004). The development of grey verhulst toolbox and the analysis of population saturation state in Taiwan-Fukien. 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04ch37583), 6, 5007–5012. https://doi.org/10.1109/icsmc.2004.1400986
51. Xiao, X., Lin, W.-Z., & Chou, K.-C. (2008). Using grey dynamic modeling and pseudo amino acid composition to predict protein structural classes. Journal of Computational Chemistry, 29(12), 2018–2024. https://doi.org/10.1002/jcc.20955
52. Yin, K., Geng, Y., & Li, X. (2018). Improved grey prediction model based on exponential grey action quantity. Journal of Systems Engineering and Electronics, 29(3), 560. https://doi.org/10.21629/jsee.2018.03.13
53. Yüceşahin, M. M. (2009). Türkiye'nin demografik geçiş sürecine coğrafi bir yaklaşım. Co, 1–25. https://doi.org/10.1501/0004993
54. Yılmaz, Y., & Karadeniz, V. (2021). Türkiye Cumhuriyeti'nin İlk Genel Nüfus Sayımına Göre Amasya İlinin Demografik Yapısı. Oltu Beşeri Ve Sosyal Bilimler Fakültesi Dergisi, 2(1), 36–51.
55. Zhang, W., Liu, S., Liu, L., Rathnayaka, R. K. T., Xie, N., & Du, J. (2023). A novel fractional-order discrete grey Gompertz model for analyzing the aging population in Jiangsu Province, China. Grey Systems: Theory and Application, 13(3), 544–557. https://doi.org/10.1108/gs-01-2023-0005
56. Zhang, Y., Xu, Y., & Wang, Z. (2009). GM(1,1) grey prediction of Lorenz chaotic system. Chaos, Solitons & Fractals, 42(2), 1003–1009. https://doi.org/10.1016/j.chaos.2009.02.031
57. Çoban, E., & İlyas, A. (2017). 1935 Nüfus Sayımı ve Bingöl'ün Nüfus Potansiyeli. Batman Üniversitesi Yaşam Bilimleri Dergisi, 7(1/1), 89–98.
58. Öztürk, Z., Bilgil, H., & Erdinç, Ü. (2022). An optimized continuous fractional grey model for forecasting of the time dependent real world cases. Hacettepe Journal of Mathematics and Statistics, 51(1), 308–326. https://doi.org/10.15672/hujms.939543
59. Şimşek, A., & Ömürbek, N. (2021). GM (1,1) Modeli ve Doğrusal Trend Analizi ile Türkiye'nin Ziyaretçi Sayısı ve Kişi Başı Ortalama Harcama Miktarı Temelinde Turizm Geliri ve Giderinin Tahmini. Gümüşhane Üniversitesi Sosyal Bilimler Dergisi, 12(2), 303–324. https://doi.org/10.36362/gumus.844179