Modeling COVID-19 pandemic with financial markets models: The case of Jaén (Spain)

Julio Guerrero; María del Carmen Galiano; Giuseppe Orlando; Julio Guerrero; María del Carmen Galiano; Giuseppe Orlando

doi:10.3934/mbe.2023399

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 9080-9100. doi: 10.3934/mbe.2023399

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Modeling COVID-19 pandemic with financial markets models: The case of Jaén (Spain)

1.
Department of Mathematics, University of Jaén, Campus de las Lagunillas s/n, Jaén 23071, Spain
2.
Department of Mathematics, University of Bari, via Edoardo Orabona 4, Bari 70125, Italy
3.
Department of Economics, HSE University, 16 Soyuza Pechatnikov Street, St Petersburg 190121, Russia

Academic Editor: Sanling Yuan

Received: 24 November 2022 Revised: 21 February 2023 Accepted: 01 March 2023 Published: 13 March 2023

The main objective of this work is to test whether some stochastic models typically used in financial markets could be applied to the COVID-19 pandemic. To this end, we have implemented the ARIMAX and Cox-Ingersoll-Ross (CIR) models originally designed for interest rate pricing but transformed by us into a forecasting tool. For the latter, which we denoted CIR*, both the Euler-Maruyama method and the Milstein method were used. Forecasts obtained with the maximum likelihood method have been validated with 95% confidence intervals and with statistical measures of goodness of fit, such as the root mean square error (RMSE). We demonstrate that the accuracy of the obtained results is consistent with the observations and sufficiently accurate to the point that the proposed CIR* framework could be considered a valid alternative to the classical ARIMAX for modelling pandemics.
- COVID-19,
- forecasting,
- Cox-Ingersoll-Ross model,
- ARIMAX,
- Milstein method
Citation: Julio Guerrero, María del Carmen Galiano, Giuseppe Orlando. Modeling COVID-19 pandemic with financial markets models: The case of Jaén (Spain)[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 9080-9100. doi: 10.3934/mbe.2023399

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Abstract

The main objective of this work is to test whether some stochastic models typically used in financial markets could be applied to the COVID-19 pandemic. To this end, we have implemented the ARIMAX and Cox-Ingersoll-Ross (CIR) models originally designed for interest rate pricing but transformed by us into a forecasting tool. For the latter, which we denoted CIR*, both the Euler-Maruyama method and the Milstein method were used. Forecasts obtained with the maximum likelihood method have been validated with 95% confidence intervals and with statistical measures of goodness of fit, such as the root mean square error (RMSE). We demonstrate that the accuracy of the obtained results is consistent with the observations and sufficiently accurate to the point that the proposed CIR* framework could be considered a valid alternative to the classical ARIMAX for modelling pandemics.

References

[1]	T. C. Mills, Time Series Techniques for Economists, Cambridge University Press, Cambridge, England, UK, 1990.
[2]	M. H. Lee, N. Hamzah, Calendar variation model based on ARIMAX for forecasting sales data with Ramadhan effect, in Proceedings of the Regional Conference on Statistical Sciences 2010 (RCSS'10), 10 (2010), 349–361.
[3]	S. Chadsuthi, C. Modchang, Y. Lenbury, S. Iamsirithaworn, W. Triampo, Modeling seasonal leptospirosis transmission and its association with rainfall and temperature in Thailand using time-series and ARIMAX analyses, Asian Pac. J. Trop. Med., 5 (2012), 539–546. https://doi.org/10.1016/S1995-7645(12)60095-9 doi: 10.1016/S1995-7645(12)60095-9
[4]	A. Suharsono, Suhartono, A. Masyitha, A. Anuravega, Time series regression and ARIMAX for forecasting currency flow at Bank Indonesia in Sulawesi region, AIP Conf. Proc., 1691 (2015). https://doi.org/10.1063/1.4937107
[5]	W. Anggraeni, R. A. Vinarti, Y. D. Kurniawati, Performance comparisons between Arima and Arimax Method in Moslem kids clothes demand forecasting: Case study, Procedia Comput. Sci., 72 (2015), 630–637. https://doi.org/10.1016/j.procs.2015.12.172 doi: 10.1016/j.procs.2015.12.172
[6]	G. Shilpa, G. Sheshadri, ARIMAX model for short-term electrical load forecasting, Int. J. Recent Technol. Eng. (IJRTE), 8 (2019), 2786–2790. https://doi.org/10.35940/ijrte.D7950.118419 doi: 10.35940/ijrte.D7950.118419
[7]	A. A. Ariyo, A. O. Adewumi, C. K. Ayo, Stock Price Prediction Using the ARIMA Model, in 2014 UKSim-AMSS 16th International Conference on Computer Modelling and Simulation, IEEE, (2014), 106–112.
[8]	G. Subramaniam, I. Muthukumar, Efficacy of time series forecasting (ARIMA) in post-COVID econometric analysis, Int. J. Stat. Appl. Math., 2020. https://doi.org/10.22271/maths.2020.v5.i6a.609
[9]	G. Orlando, M. Bufalo, Modelling bursts and chaos regularization in credit risk with a deterministic nonlinear model, Finance Res. Lett., 47 (2022), 102599. https://doi.org/10.1016/j.frl.2021.102599 doi: 10.1016/j.frl.2021.102599
[10]	G. Orlando, M. Bufalo, R. Stoop, Financial markets' deterministic aspects modeled by a low-dimensional equation, Sci. Rep., 12 (2022), 1–13. https://doi.org/10.1038/s41598-022-05765-z doi: 10.1038/s41598-022-05765-z
[11]	G. Orlando, R. M. Mininni, M. Bufalo, A new approach to CIR short-term rates modelling, in New Methods in Fixed Income Modeling, Springer, (2018), 35–43. https://doi.org/10.1007/978-3-319-95285-7_2
[12]	Y. Mishura, A. Yurchenko-Tytarenko, Standard and fractional reflected Ornstein–Uhlenbeck processes as the limits of square roots of Cox–Ingersoll–Ross processes. Stochastics, 95 (2022), 99–117. https://doi.org/10.1080/17442508.2022.2047188
[13]	O. O. Aalen, H. K. Gjessing, Survival models based on the Ornstein-Uhlenbeck process, Lifetime Data Anal., 10 (2004), 407–423. https://doi.org/10.1007/s10985-004-4775-9 doi: 10.1007/s10985-004-4775-9
[14]	A. Ekinci, Modelling and forecasting of growth rate of new COVID-19 cases in top nine affected countries: Considering conditional variance and asymmetric effect, Chaos, Solitons Fractals, 151 (2021), 111227. https://doi.org/10.1016/j.chaos.2021.111227 doi: 10.1016/j.chaos.2021.111227
[15]	A. K. Sahai, N. Rath, V. Sood, M. P. Singh, ARIMA modelling & forecasting of COVID-19 in top five affected countries, Diabetes Metab. Syndr. Clin. Res. Rev., 14 (2020), 1419–1427. https://doi.org/10.1016/j.dsx.2020.07.042 doi: 10.1016/j.dsx.2020.07.042
[16]	R. Katoch, A. Sidhu, An application of ARIMA model to forecast the dynamics of COVID-19 epidemic in India, Global Bus. Rev., 2021 (2021). https://doi.org/10.1177/0972150920988653
[17]	Suhartono, M. H. Lee, D. D. Prastyo, Two levels ARIMAX and regression models for forecasting time series data with calendar variation effects, AIP Conf. Proc., 1691 (2015). https://doi.org/10.1063/1.4937108
[18]	A. Tanyavutti, U. Tanlamai, ARIMAX versus Holt Winter methods: the case of blood demand prediction in Thailand, Int. J. Environ. Sci. Educ., 13 (2018), 519–525.
[19]	J. C. Cox, J. E. Ingersoll Jr, S. A. Ross, A theory of the term structure of interest rates, Econometrica, 53 (1985), 385–407. https://doi.org/10.2307/1911242 doi: 10.2307/1911242
[20]	J. C. Cox, J. E. Ingersoll Jr, S. A. Ross, A theory of the term structure of interest rates, in Theory of Valuation, 2nd Edition, Singapore, World Scientific, (2005), 129–164. https://doi.org/10.1142/9789812701022_0005
[21]	O. Vasicek, An equilibrium characterization of the term structure, J. Financ. Econ., 5 (1977), 177–188. https://doi.org/10.1016/0304-405X(77)90016-2 doi: 10.1016/0304-405X(77)90016-2
[22]	A. V. Chechkin, F. Seno, R. Metzler, I. M. Sokolov, Brownian yet non-gaussian diffusion: From superstatistics to subordination of diffusing diffusivities, Phys. Rev. X, 7 (2017), 021002. https://doi.org/10.1103/PhysRevX.7.021002 doi: 10.1103/PhysRevX.7.021002
[23]	W. Wang, A. G. Cherstvy, A. V. Chechkin, S. Thapa, F. Seno, X. Liu, et al. Fractional Brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time, J. Phys. A: Math. Theor., 53 (2020), 474001. https://doi.org/10.1088/1751-8121/aba467 doi: 10.1088/1751-8121/aba467
[24]	S. Ritschel, A. G. Cherstvy, R. Metzler, Universality of delay-time averages for financial time series: analytical results, computer simulations, and analysis of historical stock-market prices, J. Phys.: Complexity, 2 (2021), 045003. https://doi.org/10.1088/2632-072X/ac2220 doi: 10.1088/2632-072X/ac2220
[25]	A. Canale, R. M. Mininni, A. Rhandi, Analytic approach to solve a degenerate parabolic PDE for the Heston model, Math. Methods Appl. Sci., 40 (2017), 4982–4992. https://doi.org/10.1002/mma.4363 doi: 10.1002/mma.4363
[26]	G. Orlando, G. Taglialatela, A review on implied volatility calculation, J. Comput. Appl. Math., 320 (2017), 202–220. https://doi.org/10.1016/j.cam.2017.02.002 doi: 10.1016/j.cam.2017.02.002
[27]	G. Ascione, F. Mehrdoust, G. Orlando, O. Samimi, Foreign exchange options on Heston-CIR model under Lévy process framework, Appl. Math. Comput., 446 (2023), 127851. https://doi.org/10.1016/j.amc.2023.127851 doi: 10.1016/j.amc.2023.127851
[28]	D. Duffie, Credit risk modeling with affine processes, J. Banking Finance, 29 (2005), 2751–2802. https://doi.org/10.1016/j.jbankfin.2005.02.006 doi: 10.1016/j.jbankfin.2005.02.006
[29]	G. Orlando, M. Bufalo, H. Penikas, C. Zurlo, Modern Financial Engineering $\vert$ Topics in Systems Engineering, World Scientific Publishing Company, Singapore, 2021.
[30]	A. R. Ward, W. Glynn, Properties of the reflected Ornstein-Uhlenbeck process, Queueing Syst., 44 (2003), 109–123. https://doi.org/10.1023/A:1024403704190 doi: 10.1023/A:1024403704190
[31]	V. Giorno, A. G. Nobile, L. M. Ricciardi, On some diffusion approximations to queueing systems, Adv. Appl. Probab., 18 (1986), 991–1014. https://doi.org/10.2307/1427259 doi: 10.2307/1427259
[32]	L. M. Ricciardi, Stochastic population theory: Diffusion processes, in Mathematical Ecology, Springer, Berlin, Germany, (1986), 191–238. https://doi.org/10.1007/978-3-642-69888-0_9
[33]	V. Giorno, A. G. Nobile, R. di Cesare, On the reflected Ornstein-Uhlenbeck process with catastrophes, Appl. Math. Comput., 218 (2012), 11570–11582. https://doi.org/10.1016/j.amc.2012.04.086 doi: 10.1016/j.amc.2012.04.086
[34]	G. Orlando, G. Zimatore, Business cycle modeling between financial crises and black swans: Ornstein-Uhlenbeck stochastic process vs Kaldor deterministic chaotic model, Chaos: Interdiscip. J. Nonlinear Sci., 30 (2020), 083129. https://doi.org/10.1063/5.0015916 doi: 10.1063/5.0015916
[35]	G. Orlando, R. M. Mininni, M. Bufalo, A new approach to forecast market interest rates through the CIR model, Stud. Econ. Finance, 37 (2019), 267–292. https://doi.org/10.1108/SEF-03-2019-0116 doi: 10.1108/SEF-03-2019-0116
[36]	G. Orlando, R. M. Mininni, M. Bufalo, Interest rates calibration with a CIR model, J. Risk Finance, 20 (2019), 370–387. https://doi.org/10.1108/JRF-05-2019-0080 doi: 10.1108/JRF-05-2019-0080
[37]	G. Orlando, R. M. Mininni, M. Bufalo, Forecasting interest rates through {V}asicek and CIR models: A partitioning approach, J. Forecasting, 39 (2020), 569–579. https://doi.org/10.1002/for.2642 doi: 10.1002/for.2642
[38]	G. Orlando, M. Bufalo, Interest rates forecasting: Between Hull and White and the CIR#—How to make a single-factor model work, J. Forecasting, 40 (2021), 1566–1580. https://doi.org/10.1002/for.2783 doi: 10.1002/for.2783
[39]	L. Ljung, System identification, in Signal Analysis and Prediction, Birkhäuser, Boston, MA, (1998), 163–173. https://doi.org/10.1007/978-1-4612-1768-8_11
[40]	MathWorks, Estimate ARMAX Model, 2022. Accessed date: 18 November 2022. Available from: https://www.mathworks.com/help/ident/ref/armax.html.
[41]	P. Stoica, Y. Selen, Model-order selection: a review of information criterion rules, IEEE Signal Process. Mag., 21 (2004), 36–47.
[42]	K. Kladívko, Maximum likelihood estimation of the Cox-Ingersoll-Ross process: the MATLAB implementation, Tech. Comput. Prague, 7 (2007).
[43]	G. N. Milstein, Approximate integration of stochastic differential equations, Theory Probab. Appl., 19 (1975), 557–562.

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