Modelling Regime-Specific Dependence Structure and Investment Risk Implications in Stock Markets using Copula-Switching GARCH-GED Models.
DOI:
https://doi.org/10.54536/ajase.v5i1.6864Keywords:
General Error Distributions, Innovations Non-linearities, Stock Returns, VolatilityAbstract
A well-known traditional GARCH model assumes normal innovations which do not adequately capture sudden variations typically caused by economic shocks or disturbances. This has necessitated the need to develop non-linear, distributional and robust models. In this study, a new set of GARCH models with smooth transition non-linearities and novel innovation distributions are developed to improve the modeling and forecasting of stock returns volatilities in the Nigeria /US stock markets’ Daily data on Heating Oil, Crude Oil, and Gasoline regular spot prices (Naira/US per Dollar) from 1985 to 2025 were obtained from the U.S. Energy Information Administration (EIA) website (https://www.eia.gov/dnav/pet/pet_pri_spt_s1_d.htm). This study was carried out using copula-based regime switching GARCH Generalized Error distribution (GED) model and a hidden Markov model. The copula switching GARCH (CoS GARCH) framework showed that the spot prices of crude oil, heating oil and gasoline demonstrated distinct patterns of volatility clustering and distributions with heavy and notable interdependence among different regimes. The estimated transition probability matrix indicated that the Markov chain associated with the volatility states displayed significant persistence. The equations for the conditional means indicated that returns were marginally different across the regimes, which aligns with the established observation that energy price returns have small means compared with their variances. The findings of the study therefore established the presence of heavy tails, clustering of volatility, structural changes, and significant interdependence in energy markets.
Downloads
References
Adenomo M.O., Awogbemi C.A., Ilori A. K., Shitu D.A., Dayo V.K., Chajire B. P., Sani Z.S., Nwikpe B. J., Tanimu M. and Paul V. B. (2024). Journal of Applied Econometrics and Statistics, 3(1-2), 2024, 79-95. https://doi:10.47509/JAES.2024.v03i01-2.05
Emenogu, C.O., Onyeka-Ubaka, L. and Akanji, A.T. (2020). Volatility modeling and Value-at-Risk analysis of Total Nigeria Plc using GARCH family models. Nigerian Journal of Financial Risk Management, 26(2), 101- 122.
Aako, S. and Alabi, J. (2019). Modeling volatility in the Nigerian stock market: Evidence from GARCH-family models, Journal of Economics and Financial Studies, 11(2), 45–58.
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987-1007. https://doi.org/10.2307/1912773
Abdalla, S. Z. S. (2012). Modeling exchange rate volatility using GARCH models: Empirical evidence from Arab countries. International Journal of Economics and Finance, 4(3), 216–229.https://doi.org/10.5539/ijef.v4n3p216
Abdulaziz, M., Yusuf, A. and Ajayi, T. (2025). Holiday effects and volatility forecasting in the Nigerian stock exchange: A comparative study of EGARCH and Prophet models. Journal of Emerging Market Finance and Economics, 12(1), 56–74.
Adamu, S. I., Yusuf, A. M. and Akeyede, I. (2021). On comparative performances of ARIMA, hybrid ARIMA-ARCH and hybrid ARIMA-GARCH models in modeling the volatility of foreign exchange. Global Scientific Journal, 9(3), 31–40.
Akeyede, I. (2021). Performance of some nonlinear time series models on non-stationary data. Benin Journal of Statistics (BJS), University of Benin, Benin City, Nigeria, 4(1), 75-89.
Aloui, C., Hammoudeh, S. and Nguyen, D. K. (2013). A time-varying copula approach to oil and stock market dependence: The case of transition economies. Energy Economics, 39, 208-221. https://doi.org/10.1016/j.eneco.2013.05.005
Andersen, T. G., Bollerslev, T., Diebold, F. X. and Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71(2), 579-625. https://doi.org/10.1111/1468-0262.00418
Ardia, D. and Hoogerheide, L. F. (2010). Bayesian estimation of the GARCH(1,1) model with Student-t innovations. Studies in Nonlinear Dynamics & Econometrics, 14(2), 1–21. https://doi.org/10.2202/1558-3708.1654
Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18(1), 1-22. https://doi.org/10.1002/jae.659
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
Charles, A. and Darné, O. (2017). Volatility persistence in crude oil markets. Energy Policy, 108, 532–545. https://doi.org/10.1016/j.enpol.2017.06.021
Creti, A., Joëts, M. and Mignon, V. (2013). On the links between stock and commodity markets’ volatility. Energy Economics, 37, 16–28. https://doi.org/10.1016/j.eneco.2012.12.014
Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339-350. https://doi.org/10.1198/073500102288618487
Jiang, Y., Liu, Y. and Zhang, L. (2017). Portfolio risk management of energy commodities: A copula-GARCH approach. Energy Economics, 66, 244 - 256. https://doi.org/10.1016/j.eneco.2017.06.014
Kang, S. H., McIver, R. and Yoon, S. M. (2017). Dynamic spillover effects among crude oil, gold, and stock markets: Evidence from the Asian region. Energy Economics, 66, 371–379. https://doi.org/10.1016/j.eneco.2017.07.007
Kang, S. H. and Yoon, S. M. (2019). Dynamic spillover effects among crude oil, refined oil, and stock markets. Economic Modelling, 77, 165–178. https://doi.org/10.1016/j.econmod.2018.12.011
Kaufmann, R. K., Dees, S., Karadeloglou, P. and Sánchez, M. (2004). Does OPEC matter? An econometric analysis of oil prices. The Energy Journal, 25(4), 67–90. https://doi.org/10.5547/ISSN0195-6574-EJ-Vol25-No4-4
Mensi, W., Hammoudeh, S., Nguyen, D. K. and Yoon, S. M. (2014). Dynamic spillovers among major energy and cereal commodity prices. Energy Economics, 43, 225–243. https://doi.org/10.1016/j.eneco.2014.03.004
Narayan, P. K. and Liu, R. (2015). A unit root model for trending time-series energy variables. Energy Economics, 50, 391–402. https://doi.org/10.1016/j.eneco.2015.06.003
Narayan, P. K. and Narayan, S. (2007). Modelling oil price volatility. Energy Policy, 35(12), 6549–6553. https://doi.org/10.1016/j.enpol.2007.07.020
Nguyen, C. T. and Nguyen, M. H. (2019). Modeling stock market volatility using GARCH models: Evidence from Vietnam. Journal of Asian Business and Economic Studies, 26(1), 2–16. https://doi.org/10.1108/JABES-12-2017-0014
Nugroho, H. A., Rahmadana, M. F. and Sari, R. R. (2023). Performance of GARCH models with non-normal distributions in modeling stock return volatility. Journal of Financial Econometrics and Risk Modelling, 15(3), 118–134.
Ogundeji, R. K., Onyeka-Ubaka, J. N. and Akanji, R. A. (2021). Bayesian GARCH models for Nigeria COVID-19 data. Annals of Mathematics and Computer Science, 4, 14–27.
Patton, A. J. (2006). Modelling asymmetric exchange rate dependence. International Economic Review, 47(2), 527–556. https://doi.org/10.1111/j.1468-2354.2006.00387.x
Patton, A. J. (2012). A review of copula models for economic time series. Journal of Multivariate Analysis, 110, pp. 4-18. https://doi.org/10.1016/j.jmva.2012.02.021
Poon, S. H. and Granger, C. W. J. (2003). Forecasting volatility in financial markets: A review. Journal of Economic Literature, 41(2), 478–539. https://doi.org/10.1257/002205103765762743
Reboredo, J. C. (2011). How do crude oil prices co-move? A copula approach. Energy Economics, 33(5), 948–955. https://doi.org/10.1016/j.eneco.2011.01.008
Reboredo, J. C. (2012). Do food and oil prices co-move? Energy Policy, 49, 456–467. https://doi.org/10.1016/j.enpol.2012.06.035
Reboredo, J. C. and Rivera-Castro, M. A. (2014). Wavelet-based evidence of the impact of oil prices on stock returns. International Review of Economics & Finance, 29, 145–176. https://doi.org/10.1016/j.iref.2013.05.007
Sadorsky, P. (2006). Modeling and forecasting petroleum futures volatility. Energy Economics, 28(4), 467–488. https://doi.org/10.1016/j.eneco.2006.04.005
Taylor, S. J. (2005). Asset price dynamics, volatility, and prediction. Princeton University Press.
Usman, A., Olowe, R. A. and Obalade, A. A. (2017). Stock market volatility and economic growth in Nigeria. International Journal of Economics and Financial Issues, 7(1), 355–365.
Vaz, E., Silva, J. and Marques, J. (2017). Forecasting stock market volatility using GARCH models with exogenous variables. International Review of Financial Analysis, 50, 73–85. https://doi.org/10.1016/j.irfa.2017.03.003
Wang, Y., Wu, C. and Yang, L. (2018). Forecasting crude oil market volatility: A Markov switching multifractal volatility approach. International Journal of Forecasting, 34(4), pp. 622–635. https://doi.org/10.1016/j.ijforecast.2018.05.004
Zhao, Y., Zhang, Y., Wei, Y. and Wang, P. (2014). Modeling the volatility of crude oil returns: A regime-switching approach. Energy Economics, 43, 53–59. https://doi.org/10.1016/j.eneco.2014.02.003
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Awogbemi Clement Adeyeye, Deebom Zorle Dum, Oyowei Esueze Augustine, Ilori Adetunji Kolawole, Akeyede Imam, Peter Bitrus, Olowu Rafiu Abiodun

This work is licensed under a Creative Commons Attribution 4.0 International License.