Modelling Malaysia stock markets using GARCH, EGARCH and copula models

Document Type : Original Manuscript


1 School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia

2 Quantitative Methods Unit, Faculty of Management, Multimedia University, 63100 Cyberjaya, Selangor, Malaysia


Copula is a favored method used to measure dependency for financial data due to its flexibility. Yet, studies about dependence structure between bivariate data especially by using time-varying copula approach is very limited. Hence, this paper will examine the dependency between KLCI-FBMHS pair by considering static and time-varying copula. Traditionally, ARCH model is used to measure the volatility. However, it failed to capture stylized facts that usually exist in financial data such as the volatility clustering and leverage effect. Thus, the study also investigates the effect of different marginal models (GARCH and EGARCH) towards dependence structure and parameter estimations. Generally, the findings reveal that KCLI-FBMHS pair have strong dependency. In addition, this study highlight that ARMA(1,0)-GARCH(1,1) and ARMA(1,0)-EGARCH(1,1) with student t distribution are well-fitted to both (KLCI and FBMHS) series, the KLCI-FBMHS pair have similar dependence structure for both static and dynamic copula models.


Akaike, H. 1974. “A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control 19: 716–23.
Aminuddin, Nurul Hanis, Ruzanna Ab Razak, and Noriszura Ismail. 2018. “Dependence Measure of Daily versus Weekly Returns.” International Journal of Engineering & Technology 7(3.20): 329–33.
Ashour, Samir K., and Mahmood A. Abdel-hameed. 2010. “Approximate Skew Normal Distribution.” Journal of Advanced Research 1: 341–50.
Aussenegg, Wolfgang, and Christian Cech. 2008. Simple Time-Varying Copula Estimation.
Bollerslev, T. 1986. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics 31: 307–27.
Chen, Kuan-heng, and Khaldoun Khashanah. 2016. “Analysis of Systemic Risk : A Vine Copula- Based ARMA-GARCH Model.” Engineering Letters 24(3): 3–8.
Dajcman, Silvo. 2013. “Dependence between Croatian and European Stock Markets – A Copula GARCH Approach.” Original scientific paper 31(2): 209–32.
Embrechts, P, A McNeil, and D Straumann. 2002. Correlation and Dependence in Risk Management: Properties and Pitfalls, in Risk Management: Value at Risk and beyond. Cambridge: Cambridge University Press.
Genest, C., K. Ghoudi, and L.-P. Rivest. 1995. “A Semiparametric Estimation Procedure of Dependence Parameters in Multivariate Families of Distributions.” Biometrika 82(3): 543–52.
Hakim, Sam, and Manochehr Rashidian. 2002. “Risk & Return of Islamic Stock Market Indexes.” In 9th Economic Research Forum Annual Conference, Sharjah, U.A.E, 1–13.
Hammoudeh, Shawkat, Walid Mensi, Juan Carlos Reboredo, and Duc Khuong Nguyen. 2014. “Dynamic Dependence of the Global Islamic Equity Index with Global Conventional Equity Market Indices and Risk Factors.” Pacific-Basin Finance Journal 30: 189–206.
Hu, Wenbo, and Alec N. Kercheval. 2006. “The Skewed T Distribution for Portfolio Credit Risk ∗.”
Jawadi, Fredj, Nabila Jawadi, and Waël Louhichi. 2014. “Conventional and Islamic Stock Price Performance: An Empirical Investigation.” International Economics 137: 73–87.
Jiang, Wei. 2012. “Using the GARCH Model to Analyze and Predict the Different Stock Markets.” Uppsala University.
Joe, Harry. 1997. Multivariate Models and Dependence Concepts. New York: Chapman and Hall, London.
Kara, Emel Kizilok, and Sibel Acik Kemaloglu. 2016. “Portfolio Optimization of Dynamic Copula Models for Dependent Financial Data Using Change Point Approach.” 64(2): 175–88.
Liew, Rong Qi, and Yuan Wu. 2013. “Pairs Trading : A Copula Approach.” Journal of Derivatives & Hedge Funds 19(1): 12–30.
Manner, Hans, and Olga Reznikova. 2011. “A Survey on Time-Varying Copulas: Specification, Simulations, and Application.” Econometric Reviews 31(6): 654–87.
McNeil, Alexander J., Rudiger Frey, and Paul Embrechts. 2005. Princeton University Press Quantitative Risk Management: Concepts, Techniques and Tools. United Kingdom: Princeton University Press.
Mensi, Walid, Shawkat Hammoudeh, Ahmet Sensoy, and Seong Min Yoon. 2016. “Analysing Dynamic Linkages and Hedging Strategies between Islamic and Conventional Sector Equity Indexes.” Applied Economics: 1–23.
Nelson, Daniel B. 1991. “Conditional Heteroskedasticity in Asset Returns: A New Approach.” Econometrica 59(2): 347–70.
Nelson, R. B. 2006. An Introduction to Copulas. New York: Springer.
Ning, Cathy. 2010. “Dependence Structure between the Equity Market and the Foreign Exchange Market-A Copula Approach.” Journal of International Money and Finance 29: 743–59.
Patton, Andrew J. 2006. “Modelling Asymmetric Exchange Rate Dependence.” International Economic Review 47(2): 527–56.
Rachev, Svetlozar T., Michael Stein, and Wei Sun. 2009. “Copula Concepts in Financial Markets.”
Rahman, Maya Puspa, Mohd Azmi Omar, and Salina H. Kassim. 2015. “Modelling the Conditional Variance and Asymmetric Response to Past Shocks in the Malaysian Bond Market.” Asian Journal of Business and Accounting 8(1): 1–38.
Razak, Ruzanna Ab, and Noriszura Ismail. 2014. “Dependence Measures in Malaysian Stock Market.” Malaysian Journal of Mathematical Sciences 8(S): 109–18.
Razak, Ruzanna Ab, Noriszura Ismail, and Nor Azliana Aridi. 2016. “Is Islamic Stock Market No Different than Conventional Stock Market? An Evidence from Malaysia.” International Business Management 10(17): 3914–20.
Schwarz, G. 1978. “Estimating the Dimension of a Model.” The Annals of Statistics 6: 461–64.
Shams, Sedigheh, and Fatemeh K. Haghighi. 2013. “A Copula-GARCH Model of Conditional Dependencies: Estimating Tehran Market Stock Exchange Value-at-Risk.” Journal of Statistical and Econometric Methods 2(2): 39–50.
Shams, Sedigheh, and Masoomeh Zarshenas. 2014. “Copula Approach for Modeling Oil and Gold Prices and Exchange Rate Co-Movements in Iran.” International Journal of Statistics and Applications 4(3): 172–75.
Sukcharoen, Kunlapath, Tatevik Zohrabyan, David Leatham, and Ximing Wu. 2014. “Interdependence of Oil Prices and Stock Market Indices: A Copula Approach.” Energy Economics 44: 331–39.