Science Journal of Applied Mathematics and Statistics

Submit a Manuscript

Publishing with us to make your research visible to the widest possible audience.

Propose a Special Issue

Building a community of authors and readers to discuss the latest research and develop new ideas.

Volatility Modelling of Stock Returns of Selected Nigerian Oil and Gas Companies

Modelling volatility asset returns is a well-researched concept in financial statistics, given its significance to investment analysts, economists, risk-averse investors, policymakers and other relevant stakeholders to underpin the market and the general economic performance and resilience to shocks, domestically and internationally. Thus, this study fits an appropriate ARCH/GARCH family model to daily stock returns volatility of each of the selected five most traded assets of the oil and gas marketing companies on the Nigerian stock exchange (NSE), using daily closing prices from January 1, 2005, to December 31, 2020. First-order symmetric and asymmetric volatility models with the Normal, Student’s t, Skewed Student’s t and generalized error distributions (GED) were fitted to select the best model with the most appropriate error distribution using appropriate model selection criteri EGARCH (1,1) with GEDs was found to be the best-fitted models based on the Akaike Information Criterion (AIC). The results indicated the presence of a leverage effect in the series and how the volatility reacts to good news as against bad news implying that positive shock has a higher impact on the returns of the respective companies. Based on the findings it is recommended that, for enhanced precision, GARCH family models with appropriate error distribution be applied in underpinning assets volatility, which in turn would help to better understand the nature of inherent shocks characterizing asset volatility of the respective companies. With such knowledge, appropriate investment decisions are made to guide risk-averse investors in their investments.

Volatility, Oil/Gas Industry, ARCH/GARCH Models, Leverage Effect, Nigerian Stock Exchange

APA Style

Maruf Ariyo Raheem, Regina Domingo Mbeke, Elisha John Inyang. (2023). Volatility Modelling of Stock Returns of Selected Nigerian Oil and Gas Companies. Science Journal of Applied Mathematics and Statistics, 11(2), 26-36.

ACS Style

Maruf Ariyo Raheem; Regina Domingo Mbeke; Elisha John Inyang. Volatility Modelling of Stock Returns of Selected Nigerian Oil and Gas Companies. Sci. J. Appl. Math. Stat. 2023, 11(2), 26-36. doi: 10.11648/j.sjams.20231102.11

AMA Style

Maruf Ariyo Raheem, Regina Domingo Mbeke, Elisha John Inyang. Volatility Modelling of Stock Returns of Selected Nigerian Oil and Gas Companies. Sci J Appl Math Stat. 2023;11(2):26-36. doi: 10.11648/j.sjams.20231102.11

Copyright © 2023 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Abdalla, S. Z. S. Suliman, Z. (2012): Modelling stock returns volatility: Empirical evidence from Saudi Stock Exchange. Int. Res. J. Finance. Econ., 85, 166–179.
2. Ahmed, A. E. M., & Suliman, S. Z. (2011). Modeling stock market volatility using GARCH models evidence from Sudan. International journal of business and social science, 2 (23).
3. Akaike, H. (1973): Information theory and an extension of the maximum likelihood principle. In B. N. Petrov and F. Csaki, (eds.). 2nd International Symposium on Information Theory, Akademia Kiado, Budapest.
4. Alberg, D.; Shalit, H.; Yosef, R (2008): Estimating stock market volatility using asymmetric GARCH models. App. Financ. Econ. 2008, 18, 1201–1208.
5. Berkes, I., Horvath, L., and Kokoskza, P. (2003): GARCH processes: Structure and estimation. Bernoulli, 9: 2001–2007, 2003. Black.
6. Bollerslev, T. (1986): Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31: 307–327.
7. Bollerslev, T., Engle, R. F., and Nelson, D. B. (1994): ARCH model. In R. F. Engle and D. C. McFadden (eds.). Handbook of Econometrics IV, pp. 2959–3038. Elsevier Science, Amsterdam.
8. Box, G. E. P. and Pierce, D. (1970): Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association 65: 1509–1526.
9. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994): Time Series Analysis: Forecasting and Control, 3rd ed. Prentice Hall, Englewood Cliffs, NJ.
10. Brockwell, P. J. and Davis, R. A. (1991): Time Series: Theory and Methods. 2nd ed. Springer, New York.
11. Brockwell, P. J. and Davis, R. A. (1996): Introduction to Time Series and Forecasting. Springer, New York.
12. CBN (2006): Annual Statistical Bulletin - Central Bank of Nigeria, Volume 17, December:
13. Dallah, H. and Ade I. (2010): Modelling and Forecasting the Volatility of the Daily Returns of Nigerian Insurance Stocks. International Business Research 3 (2): 106-116.
14. Dickey, D. A. and Fuller, W. A. (1979): Distribution of the estimates for autoregressive time series with a unit root. Journal of the American Statistical Association 74: 427–431.
15. Ekum, M. I., Owolabi, T. O. and Alakija, T. (2018): Modeling Volatility in Selected Nigerian Stock Market. International Journal of Economics and Financial Management Vol. 3 No. 1 2018 ISSN: 2545–5966.
16. Engle, R. F. (1982): Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflations. Econometrica 50: 987–1007.
17. Girard, E.; Omran, M.(2009): On the relationship between trading volume and stock price volatility in CASE. Int. J. Manag. Financ., 5, 110–134.
18. Goldman, E., & Shen, X. (2017). Analysis of asymmetric GARCH volatility models with applications to margin measurement. Pace University Finance Research Paper, (2018/03).
19. Jarque, C. M. and Bera, A. K. (1987): A test of normality of observations and regression residuals. International Statistical Review 55: 163–172.
20. Jayasuriya, S. (2002): Does Stock Market Libralisation Affect the Volatility of Stock Returns? Evidence from Emerging Market Economies. Georgetown University Discussion Series.
21. Joshi, P. (2010): Modeling volatility in emerging stock markets of India and China. J. Q. Econ. 2010, 8, 86–94.
22. Liu, H. C.; Hung, J. C. (2010): Forecasting S&P-100 stock index volatility: The role of volatility asymmetry and distributional assumption in GARCH models. Expert Syst. Appl. 2010, 37, 4928–4934.
23. Liu, L., Geng, Q., Zhang, Y., & Wang, Y. (2021). Investors’ perspective on forecasting crude oil return volatility: Where do we stand today? Journal of Management Science and Engineering.
24. Nelson, D. B. (1991): Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59: 347–370.
25. Neokosmidis, I. (2009): Econometric Analysis of Realized Volatility: Evidence of Financial Crisis. pp. 1–22.
26. Ogum, G. Beer, F and Nouyrigat, G. (2005): Emerging Equity Market Volatility: An Empirical Investigation of Markets in Kenya and Nigeria. Journal of African Business 6 (1/2): 139-154.
27. Olowe, R. A. (2009): Stock return volatility, global financial crisis and the monthly seasonal effect on the Nigerian stock exchange. Afr. Rev. Money Financ. Bank., 73–107.
28. Raheem, M. A. and Ezepue, P. O. (2018) Some Stylized Facts of Short-Term Stock Prices of Selected Nigerian Banks. Open Journal of Statistics, 8, 94-133.
29. Rao, S. S. (2016): A course in Time Series Analysis. Email:, November 30, 2016.
30. Ruey S. T. (2010): Analysis of Financial Time Series. 3rd Edition, A John Wiley & Sons, Inc., Publication, Chicago.
31. Shalini, A. P. (2014): An empirical study of volatility of sectoral indices (India). Indian Res. J. 2014, 1, 78–95.
32. Shanthi, A.; Thamilselvan, R. (2019): Univariate GARCH models applied to the Bombay stock exchange and national stock exchange stock indices. Int. J. Manag. Bus. Res. 2019, 9, 22–33.
33. So, M. K., Chu, A. M., Lo, C. C., & Ip, C. Y. (2021). Volatility and dynamic dependence modeling: Review, applications, and financial risk management. Wiley Interdisciplinary Reviews: Computational Statistics, e1567.
34. Tripathy, T.; Gil-Alana, L. A. (2010): Suitability of volatility models for forecasting stock market returns: A study on the Indian National Stock Exchange. Am. J. Appl. Sci., 7, 1487–1494. 32.
35. Tsay, R. S. (2012): An Introduction to Analysis of Financial Data with R. Wiley Publishing.
36. Wong, A.; Cheung, K. Y. (2011): Measuring and visualizing the asymmetries in stock market volatility: Case of Hong Kong. Int. Res. J. Appl. Finance. 2 (35) 1–26.