Sains Malaysiana 51(7)(2022): 2249-2264

http://doi.org/10.17576/jsm-2022-5107-25

Performance of a Novel Hybrid Model through Simulation and Historical Financial Data

(Prestasi Model Hibrid Novel melalui Simulasi dan Data Kewangan Sejarah)

MD. JAMAL HOSSAIN^1,2 & MOHD TAHIR ISMAIL³

¹School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Pulau Pinang, Malaysia

²Department of Applied Mathematics, Noakhali Science and Technology University, Noakhali-3814, Bangladesh

³School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Pulau Pinang, Malaysia

Received: 24 May 2021/Accepted: 1 January 2022

Abstract

It is thoroughly acknowledged that the historical financial time series is not linear, exhibits structural changes, and is volatile. It has been noticed in the current literature that because of the existence of structural breaks in the historical time series, the GARCH family models provide misleading results and poor forecasts. Thus, it is unavoidable to incorporate models with nonlinearity in the conditional mean and conditional variance to capture volatility dynamics more precisely than the existing models. Therefore, inspiring in this matter, this study proposes a novel hybrid model of exponential autoregressive (ExpAR) with a Markov-switching GARCH (MSGARCH) model. This study also examines volatility dynamics and performances through simulation and real-world financial data. Moreover, this study investigates downside risk management performances using 5% VaR (Value-at-Risk) back-testing. The empirical findings showed that the proposed model outperforms the benchmark model for both simulation and real-world time series data. The VaR results also showed that the proposed model captures downside risk more meticulously than the benchmark model.

Keywords: ExpAR model; ExpAR-MSGARCH model; MSGARCH model; structural breaks; value-at-risk

Abstrak

Diakui secara benar bahawa siri masa kewangan masa lampau adalah tidak linear, menunjukkan perubahan struktur dan meruap. Dapat dilihat dalam kepustakaan semasa oleh kerana adanya putusan berstruktur dalam siri masa lampau, model keluarga GARCH memberikan hasil yang tidak benar dan ramalan yang lemah. Oleh itu, tidak dapat dielak untuk menggabungkan model yang tidak linear pada min dan varians bersyarat untuk menguasai dinamik kemeruapan dengan lebih tepat daripada model sedia ada. Maka, berinspirasi daripada hal ini, kajian ini mencadangkan model hibrid baharu eksponen autoregresif (ExpAR) dengan model pertukaran Markov GARCH (MSGARCH). Kajian ini juga mengkaji prestasi dan dinamik kemeruapan melalui simulasi dan data kewangan dunia yang betul. Lebih-lebih lagi, penyelidikan ini mengkaji prestasi pengurusan risiko penurunan menggunakan ujian semula 5% VaR (risiko pada nilai). Penemuan empirik menunjukkan bahawa model yang dicadangkan mengungguli model penanda aras untuk kedua-dua simulasi dan data siri masa yang betul. Hasil VaR juga menunjukkan bahawa model yang dicadangkan menangkap risiko penurunan lebih teliti daripada model penanda aras.

Kata kunci: Model ExpAR; model ExpAR-MSGARCH; model MSGARCH; putusan berstruktur; risiko pada nilai

REFERENCES

Abdollahi, H. & Ebrahimi, S.B. 2020. A new hybrid model for forecasting Brent crude oil price. Energy 200: 117520.

Abdulsalam, F. & Bouresli, A. 2019. Price-volume relation behavior around structural breaks in Kuwait Boursa. Innovative Marketing 15(2): 1-13.

Ali, M.H., Uddin, M.A., Chowdhury, M.A.F. & Masih, M. 2019. Cross-country evidence of Islamic portfolio diversification: Are there opportunities in Saudi Arabia? Managerial Finance 45(1): 36-53.

Allal, J. & El Melhaoui, S. 2006. Optimal detection of exponential component in autoregressive models. Journal of Time Series Analysis 27(6): 793-810.

Amiri, E. 2012. Forecasting GDP growth rate with nonlinear models. 1st International Conference on Econometrics Methods and Applications. hlm. 25-27.

Ardia, D., Bluteau, K., Boudt, K. & Catania, L. 2018. Forecasting risk with Markov-switching GARCH models: A large-scale performance study. International Journal of Forecasting 34(4): 733-747.

Arellano, M.A. & Rodríguez, G. 2020. Empirical modeling of high-income and emerging stock and Forex market return volatility using Markov-switching GARCH models. North American Journal of Economics and Finance 52(October 2018): 101163.

Baragona, R., Battaglia, F. & Cucina, D. 2002. A note on estimating autoregressive exponential models. Quaderni di Statistica 4: 1-18.

Bauwens, L., De Backer, B. & Dufays, A. 2014. A Bayesian method of change-point estimation with recurrent regimes: Application to GARCH models. Journal of Empirical Finance 29: 207-229.

Bollerslev, T. 1986. Generalized auroregressive conditional hetroskedasticity. Journal of Econometrics 31: 307-327.

Box, G.E. & Jenkins, G.M. 1970. Time series analysis: Forecasting and control. Holden-Day: Oakland, California.

Chan, K.S. & Tong, H. 1986. On estimating thresholds in autoregressive models. Journal of Time Series Analysis 7(3): 179-190.

Christoffersen, P.F. 1998. Evaluating interval forecasts. International Economic Review 39(4): 841-862.

Danielsson, J. 2011. Risk and Crises. https://voxeu.org/article/risk-and-crises-how-models-failed-and-are-failing.

Engle, R.F. 1982. Autoregressive conditional heteroscedacity with estimates of variance of United Kingdom inflation. Econometrica 50(4): 987-1007.

Engle, R.F. & Manganelli, S. 2004. CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics 22(4): 367-381.

Gao, G., Ho, K.Y. & Shi, Y. 2020. Long memory or regime switching in volatility? Evidence from high-frequency returns on the U.S. stock indices. Pacific Basin Finance Journal 61(July 2018): 101059.

Ghosh, H., Gurung, B. & Gupta, P. 2014. Fitting EXPAR models through the extended Kalman filter. Sankhya B 77(1): 27-44.

Granger, C.W. & Andersen, A.P. 1978. An Introduction to Bilinear Time Series Models. Gottingen: Vandenhoeck and Ruprecht. p. 94.

Haas, M., Mittnik, S. & Paolella, M.S. 2004. A new approach to markov-switching GARCH models. Journal of Financial Econometrics 2(4): 493-530.

Haggan, V. & Ozaki, T. 1981. Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68(1): 189-196.

Hamilton, J.D. 1994. Time Series Analysis. 1 ed. Princeton: Princeton University Press.

Hansen, P.R. & Lunde, A. 2005. A forecast comparison of volatility models: Does anything beat a GARCH(1,1)? Journal of Applied Econometrics 20(7): 873-889.

Herrera, A.M., Hu, L. & Pastor, D. 2018. Forecasting crude oil price volatility. International Journal of Forecasting 34(4): 622-635.

Hossain, M.J. & Ismail, M.T. 2021. Is there any influence of other cryptocurrencies on bitcoin? Asian Academy of Management Journal of Accounting and Finance 17(1): 125-152.

Hull, J.C. 2018. Risk Management and Financial Institutions. 5 ed. John New Jersey: Wiley & Sons, Inc.

Ishizuka, K., Kato, H. & Nakatani, T. 2005. Speech signal analysis with exponential autoregressive model. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings I. pp. 225-228.

Katsiampa, P. 2014. A new approach to modelling nonlinear time series: Introducing the ExpAR-ARCH and ExpAR-GARCH models and applications. OpenAccess Series in Informatics 37: 34-51.

Kupiec, P.H. 1995. Techniques for verifying the accuracy of risk measurement models. The Journal of Derivatives 3(2): 73-84.

Lin, Y., Xiao, Y. & Li, F. 2020. Forecasting crude oil price volatility via a HM-EGARCH model. Energy Economics 87: 104693.

Marcucci, J. 2005. Forecasting stock market volatility with regime-switching GARCH models. Studies in Nonlinear Dynamics and Econometrics 9(4): 159-213.

Meitz, M. & Saikkonen, P. 2008. Stability of nonlinear AR-GARCH models. Journal of Time Series Analysis 29(3): 453-475.

Merzougui, M. 2017. Estimation in periodic restricted EXPAR(1) models. Communications in Statistics: Simulation and Computation 47(10): 2819-2828.

Merzougui, M., Dridi, H. & Chadli, A. 2016. Test for periodicity in restrictive EXPAR models. Communications in Statistics - Theory and Methods 45(9): 2770-2783.

Mohammadi, H. & Su, L. 2010. International evidence on crude oil price dynamics: Applications of ARIMA-GARCH models. Energy Economics 32(5): 1001-1008.

Moritz, S. & Bartz-Beielstein, T. 2017. imputeTS: Time series missing value imputation in R. R Journal 9(1): 207-218.

Ozaki, T. 1980. Non-Linear time series models for non-linear random vibrations. Journal of Applied Probability 17(1): 84-93.

Ozaki, T. & Oda, H. 1977. Non-Linear time series model identification by Akaike’s information criterion. IFAC Proceedings Volumes 10(12): 83-91.

Rahim, M.A.I.A., Zahari, S.M. & Shariff, S.S.R. 2018. Variance targeting estimator for GJR-GARCH under model’s misspecification. Sains Malaysiana 47(9): 2195-2204.

Theiri, S. & Ati, A. 2020. Weak form of efficiency hypotheses: Empirical modeling with box-Pierce, ADF and ARCH tests. International Journal of Financial Research 11(5): 137-149.

Tong, H. 1990. Non-Linear Time Series: A Dynamical System Approach. Oxford University Press.

Tong, H. 1978. On a threshold model. In Pattern Recognition and Signal Processing, edited by Chen, C.H. The Netherlands: Sijthoff & Noordhoff. pp. 575-586.

Tong, H. & Lim, K.S. 1980. Threshold autoregression, limit cycles and cyclical data. Journal of the Royal Statistical Society. Series B (Methodological) 42(3): 245-292.

Xu, H., Wan, L., Ding, F., Alsaedi, A. & Hayat, T. 2019. Fitting the exponential autoregressive model through recursive search. Journal of the Franklin Institute 356(11): 5801-5818.

Zahid, M. & Iqbal, F. 2020. Modeling the volatility of cryptocurrencies: An empirical application of stochastic volatility models. Sains Malaysiana 49(3): 703-712.

^*Corresponding author; email: z_math_du@yahoo.com