Modelling the oil price volatility and macroeconomic variables in South Africa using MGARCH Models

Abstract

This study modelled the oil price volatility and macroeconomic variables in South Africa using Multivariate GARCH models. The data used in the study consists of 114 observations ranging from 1990 Q1 to 2018 Q2. The study assessed the oil price volatility with the independent variables being the macroeconomic variables (GDP, Inflation, Interest rate and Exchange rates) using the ARCH, GARCH, EGARCH and Multivariate GARCH-BEKK models. The importance of this study is on determining relationship between oil price volatility and macroeconomic variables as it is one of the impacts driving the economic growth of South Africa due to the fact that South Africa depends on imported crude oil and cannot control oil prices. The results of the ADF and PP tests revealed that all the variables are stationary at first difference. That is integrated to order 1, I (1). Furthermore, the study presented the QQ plot as an important diagnostic test for checking the assumption of normality. The variables passed the diagnostic checks and can be used for further analysis. The results from the ARCH model was found to be statistically significant which means that the equation could be modelled using the GARCH technique. The LM test also confirmed the use of GARCH technique. The GARCH (1.1) model was fitted and the results revealed that exchange rate and interest rate have a negative effect on oil price while GDP and inflation suggested a positive effect. The sum of ∝ and β was found to be greater than 1. This means that the South African oil price is volatile. The diagnostic test for the GARCH model revealed that the model is adequate and can be used for further analysis. The results from the EGARCH (1.1) model revealed that oil price is found to be negatively related to all the macroeconomic variables. This means that a 1% increase in macroeconomic variables may lead to a decrease in oil price. The diagnostic checks showed that the macroeconomic variables on oil price have no ARCH errors. Furthermore, the EGARCH model appeared to be adequate and was used for further analysis.

The Multivariate GARCH model was also examined using the BEKK-GARCH model. The results revealed that all the estimates of the diagonal parameters are statistically significant at 5% level of significance. The residual series of the model portrayed a certain pattern for each of the macroeconomic variables. However, the BEKK-GARCH model showed the presence of autocorrelation in the residuals. The study found that there is no spill-over effect between oil price and the two macroeconomic variables (inflation and exchange rate). The study also found that there is a unidirectional volatility transmission between oil price and GDP; oil price and inflation; oil price and interest rate; oil price and exchange rate; GDP and interest rate; inflation and interest rate; and inflation and exchange rate. The study contributes to the existing literature on modelling oil price volatility and macroeconomic variables using the GARCH and the Multivariate GARCH models. The study also provided recommendations for future studies.