ABSTRACT. This paper focuses on volatility modeling of the Johannesburg Stock Exchange (JSE) all share index and risk estimation using the Bayesian and frequentist approaches. A Bayesian Autoregressive Moving Average-Generalized Autoregressive Conditional Heteroskedasticity (BARMA-GARCH-t) modeling of the All Share Index (ALSI) at the Johannesburg Stock Exchange (JSE) under the assumption of Student-t innovations is presented. The ALSI data is for the years 2002 to 2013. Uncertainty about the true values of the GARCH parameters is incorporated into the analysis through a non-informative joint prior distribution. A comparative analysis is done with a standard GARCH model with Student-t innovations (ARMA-GARCH-t) using the maximum likelihood (ML) method. Empirical results from this study show that BARMA-GARCH-t model captures well both the conditional and unconditional volatilities of the ALSI share index at the JSE. The BARMA-GARCH-t model provides a better fit to the data compared to the bench mark model which is the ARMA-GARCH-t model. The results are important to stock brokers, risk and investment managers. pp. 33–48
JEL codes: C4; C53; G1

Keywords: Bayes; GARCH; portfolio management; Student-t distribution; risk management

How to cite: Sigauke, Caston (2016), “Volatility Modeling of the JSE All Share Index and Risk Estimation Using the Bayesian and Frequentist Approaches,” Economics, Management, and Financial Markets 11(4): 33–48.

Received 8 April 2015 • Received in revised form 7 November 2015
Accepted 8 November 2015 • Available online 25 January 2016

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Department of Statistics,
University of Venda

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