Comparative Forecasting of Some Key Economic Indicators Using Artificial Neural Networks and Ordinary Differential Equations: A Case Study of the Turkish Economy

Abstract

This study explores the relationships between the USD opening exchange rate, the annual change rate of the Consumer Price Index (CPI), the housing loan interest rate in Turkish lira, and the residential construction cost index from January 2015 to May 2024 using data from the Turkish Statistical Institute (TUIK). Artificial Neural Networks (ANN) and Ordinary Differential Equations (ODE) methods were employed to model the interactions among these four variables. In the ANN approach, each variable was modeled as the dependent variable in turn, with the remaining three serving as independent variables, resulting in four distinct analyses. The ODE model, on the other hand, provided a holistic analysis by capturing the time-dependent relationships among all four variables simultaneously. The ANN model predictions achieved accuracy rates of 87.2% for the USD opening exchange rate, 91.4% for the CPI annual change rate, 85.9% for the housing loan interest rate, and 93.1% for the construction cost index. Meanwhile, the ODE model demonstrated its strength by offering a more comprehensive framework with an overall accuracy of 94.6%, effectively capturing the complex interdependencies among the variables. These findings highlight the strengths of both approaches: while the ANN model excels in analyzing individual variables, the ODE model offers a broader perspective by integrating all variables into a unified framework. This study contributes to developing economic forecasting models and provides valuable insights for decision-makers, particularly in times of economic uncertainty.

Keywords

• Turkish economy
• artificial neural networks
• ordinary differential equations
• comparative forecasting

References

1. N. Frumkin, Guide to economic indicators, 4th Edition, New York, 2015.
2. M. K. Heun, J. Santos, P. E. Brockway, R. Pruim, T. Domingos, M. Sakai, From theory to econometrics to energy policy: Cautionary tales for policymaking using aggregate production functions, Energies 10 (2) (2017) Article Number 203 44 pages.
3. D. Güneş, İ. Özkan, L. Erden, Economic sentiment and foreign portfolio flows: Evidence from Türkiye, Central Bank Review 24 (1) (2024) 100147 9 pages.
4. P. Chinnasamy, A. Albakri, M. Khan, A. A. Raja, A. Kiran, J. C. Babu, Smart contract-enabled secure sharing of health data for a mobile cloud-based e-health system, Applied Sciences 13 (6) (2023) 3970 19 pages.
5. M. Khan, S. Hariharasitaraman, S. Joshi, V. Jain, M. Ramanan, A. SampathKumar, A. A. Elngar, A deep learning approach for facial emotions recognition using principal component analysis and neural network techniques, The Photogrammetric Record 37 (180) (2022) 435–452.
6. T. V. Ramana, G. S. Ghantasala, R. Sathiyaraj, M. Khan, Artificial intelligence and machine learning for smart community; concepts and applications, CRC Press, Florida, 2024.
7. J. Zou, Y. Han, S. S. So, Overview of artificial neural networks, Artificial Neural Networks: Methods and Applications 458 (2009) 14–22.
8. P. Hartman, Ordinary differential equations, Society for Industrial and Applied Mathematics, Philadelphia, 2002.

9. B. Zheng, Ordinary Differential equation and its application, Highlights in Science, Engineering and Technology 72 (2023) 645–651.
10. E. Alshawarbeh, A. T. Abdulrahman, E. Hussam, Statistical modeling of high frequency datasets using the ARIMA-ANN hybrid, Mathematics 11 (22) (2023) 4594 17 pages.
11. A. R. Mohamed, Artificial neural network for modeling the economic performance: A new perspective, Journal of Quantitative Economics 20 (3) (2022) 555–575.
12. G. W. R. I. Wijesinghe, R. M. K. T. Rathnayaka, Stock market price forecasting using ARIMA vs ANN: A case study from CSE, In 2020 2nd International Conference on Advancements in Computing (ICAC), IEEE, 2020, Vol. 1, pp. 269–274.
13. K. M. Ramírez, J. M. Hormaza, S. V. Soto, Artificial intelligence and its impact on the prediction of economic indicators, In Proceedings of the 6th International Conference on Engineering and MIS, 2020, pp. 1–8.
14. M. Fani, N. Norouzi, Using social and economic indicators for modeling, sensitivity analysis and forecasting the gasoline demand in the transportation sector: an ANN Approach in case study for Tehran metropolis, Iranian Journal of Energy 23 (2) (2020) 71–91.
15. L. Guerrini, A. Krawiec, M. Szydlowski, Bifurcations in an economic growth model with a distributed time delay transformed to ODE, Non-Linear Dynamics 101 (2) (2020) 1263–1279.
16. L. Wu, X. Qiu, Y. X. Yuan, H. Wu, Parameter estimation and variable selection for big systems of linear ordinary differential equations: A matrix-based approach, Journal of the American Statistical Association 114 (526) (2019) 657–667.
17. I. Georgiev, V. Centeno, V. Mihova, V. Pavlov, A modified ordinary differential equation approach in price forecasting, in AIP conference proceedings, AIP Publishing 2459 (1) (2022) 030008 7 pages.
18. B. Daşbaşı, İ. Öztürk, The dynamics between pathogen and host with Holling type 2 response of immune system, Journal Of Graduate School of Natural and Applied Sciences 32 (1) (2016) 1–10.
19. S. Paul, A. Mahata, S. Mukherjee, M. Das, P. C. Mali, B. Roy, P. Bharati, Study of fractional order SIR model with MH type treatment rate and its stability analysis, Bulletin of Biomathematics 2 (1) (2024) 85–113.
20. R. B. Guenther, J. W. Lee, Partial differential equations of mathematical physics and integral equations, Courier Corporation, New Jersey, 1996.
21. K. Sobczyk, Stochastic differential equations: with applications to physics and engineering, Springer Science and Business Media, Dordrecht, 2013.
22. B. Daşbaşı, Fractional order bacterial infection model with effects of anti-virulence drug and antibiotic, Chaos, Solitons and Fractals 170 (2023) 113331 17 pages.
23. H. Niu, Y. Zhou, X. Yan, J. Wu, Y. Shen, Z. Yi, J. Hu, On the applications of neural ordinary differential equations in medical image analysis, Artificial Intelligence Review 57 (9) (2024) 236 32 pages.
24. B. Daşbaşi, T. Daşbaşi, Mathematical analysis of Lengyel-Epstein chemical reaction model by fractional-order differential equations system with multi-orders, International Journal of Science and Engineering Investigations 6 (11) (2017) 78–83.
25. N. Manhas, Mathematical model for IP33 dependent calcium oscillations and mitochondrial associate membranes in non-excitable cells, Mathematical Modelling and Numerical Simulation with Applications 4 (3) (2024) 280–295.
26. E. Sönmez, B. Daşbaşı, T. Daşbaşı, Some applications on stability analysis of incommensurate and commensurate fractional-order differential equation systems: Brusselator chemical reaction model and bacterial infection model, Academic Studies in Physics and Mathematics from Theory to Application II, Chapter 10, IKSAD Publishing House, 2022.
27. B. Goodwine, Engineering differential equations: theory and applications, Springer Science and Business Media, 2010.
28. K. S. Miller, Partial differential equations in engineering problems, Courier Dover Publications, New Jersey, 2020.
29. B. Ersoy, B. Daşbaşı, E. Aslan, Mathematical modelling of fiber optic cable with an electro-optical cladding by incommensurate fractional-order differential equations, An International Journal of Optimization and Control: Theories and Applications 14 (1) (2024) 50–61.
30. R. Boucekkine, G. Fabbri, P. Pintus, On the optimal control of a linear neutral differential equation arising in economics, Optimal Control Applications and Methods 33 (5) (2012) 511–530.
31. M. D. Johansyah, A. K. Supriatna, E. Rusyaman, J. Saputra, Application of fractional differential equation in economic growth model: A systematic review approach, AIMS Mathematics 6 (9) (2021) 10266–10280.
32. Z. Hosseini-Nodeh, R. Khanjani-Shiraz, P. M. Pardalos, Portfolio optimization using robust mean absolute deviation model: Wasserstein metric approach, Finance Research Letters 54 (2023) 103735 13 pages.
33. Z. Wang, A. C. Bovik, Mean squared error: Love it or leave it? A new look at signal fidelity measures, IEEE Signal Processing Magazine 26 (1) (2009) 98–117.
34. T. O. Hodson, Root means square error (RMSE) or mean absolute error (MAE): When to use them or not, Geoscientific Model Development Discussions, 15 (2022) 5481–5487.
35. E. Işık, B. Daşbaşı, A compartmental fractional-order mobbing model and the determination of its parameters, Bulletin of Biomathematics 1 (2) (2023) 153–176.