Modelling South African official gold reserves position, and foreign exchange reserves position using time series models.

Abstract

Every central bank of the country should hold enough reserves such as foreign exchange currency, gold, or any form of reserves to be able to help its country in times of difficulties or financial crises. This involves the process of ensuring that adequate official public sector foreign assets are readily available to meet any defined range of objectives by a country. Reserves can also play a pivotal role in supporting and maintaining confidence in the policies for monetary and exchange rate management, including the ability to intervene in the foreign market to influence the value of the local currency. It can also be used to provide proof to the market that a country can meet its current and future external obligations, limit external exposure by maintaining foreign currency liquidity to absorb shock during times of crisis, show the support of domestic currency by external assets, assist the government in meeting its foreign exchange needs and external debt obligations, and maintain sufficient reserves for national disasters or emergencies. All this cannot be done without the understanding of all factors that affect reserves of the country, hence careful analysis of reserves in a country plays a crucial role on how the central bank should manage the reserves of such a country. This includes a wide range of social, economic, and statistical analyses. However, this study focuses more on the statistical analysis part, which is, building models to predict or forecast the trajectory of reserves positions in future. These models should be able to consider all the factors that influence the reserves, such as trend, seasonality and the variability (random variability). The Seasonal ARIMA models were used as initial models to forecast the future reserves positions. Seasonal ARIMA Generalized Autoregressive Conditional Heteroskedasticity models with Skewed Student-t Distribution (SARIMA – GARCH – SSTD) were also used to forecast volatility from the foreign exchange reserves data after statistical test were carried out and the data was found to have ARCH Effects. The best volatility model that was found to produces best forecast for foreign exchange reserves data was the SARIMA (0,1,0) (2,1,0)12 – GARCH (1,1) – SSTD model. The SARIMA model developed earlier for gold reserves data was then benchmarked with the Holt-Winters' Seasonal method. The results from the analysis showed that SARIMA model outperformed Holt-Winters' Seasonal method in forecasting gold reserves positions. We found that future gold reserves positions can be better predicted using the SARIMA (1,1,0) (0,1,2)12 model. The best model was selected from many other models using model diagnostics process such as comparisons of the AIC, RMSE, number of significant parameters and the evaluation of residuals to identify their flexibility. Using the forecasting methods developed in this study, the central bank can better understand what to expect in the future and decide on what measures to implement for national economic stability.