Exchange rate volatility in South Africa: a comparative analysis of the ARCH and GARCH models

Abstract

In SA, the Rand has been particularly volatile over the course of the 1990s. For a count1y that depends largely on foreign trade like SA, during periods of excessive volatility in exchange rate, foreign trade and investments are affected negatively. The main purpose of this study was to assess exchange rate volatility in SA. It was important to investigate this subject since volatility in the exchange rate causes lot of uncertainties in terms of foreign investment and therefore macroeconomic factors such as GDP, INTR and INF are affected negatively. The study applied ARCH (1), GARCH (1,1) and GARCH (1,2) models to assess exchange rate volatility in SA. These models were constructed using four variables; namely, exchange rate (ER), gross domestic product (GDP), inflation rate (INF) and interest rate (INTR). Quarterly time series data from the year I990:QI until 2014:Q2 was sourced from SARB and OECD databases. The period was considered mainly because it captures the 2007 and 2008 financial crisis and also gives a clear picture of what happened after the apartheid era. E-Views 8 version was used to obtain results. A detailed analysis for ARCH (I), GARCH (1,1) and GARCH (1,2) model estimation was given. Prior to estimating the models, preliminary data analysis was conducted to check variable description. All the variables passed the diagnostics such as independence, unit root and normality. This stage was followed up with primary data analysis applying ARCH (I), GARCH (1,1) and GARCH (1,2) frameworks. Three models were constructed and subjected to model diagnostics testing. GARCH (1,1) model was found to be fit and stable for the data. This model was recommended for further analysis and was later used for producing forecasts of exchange rate volatility in SA for the period 2014:Q3 and 2020:Q4. The ER volatility forecasts showed consistency when compared to the past values proving that GARCH (1,1) was suitable and valid for forecasting. The model further produced a high volatility constant compared to other models. GARCH (1,1) - BEKK and GARCH (1,1) -CCC models were also applied to check volatility spill over effects and conditional volatilities among variables. All variables for both models were statistically significant at 5% level of significance except for ER. The GARCH (1,1) - BEKK model indicated a high volatility spill over effect for all variables while the GARCH (1,1) - CCC indicated an independent relationship between the conditional volatilities for all variables except for ER. Based on these findings, the study recommended the use of this model to do further forecasting. These forecasts may be used when embarking on new policies concerning exchange rate in the count1y. A follow-up study was recommended where other GARCH family models will be estimated and the results compared with those obtained in this study.