Abstract
The economy of Botswana heavily relies on mineral exports (mainly diamond exports), which are largely dependent on the exchange rate. And, the US Dollar is one of the most important currencies in the basket of currencies to which the Botswana Pula is pegged. Therefore, this paper seeks to empirically establish the baseline characteristics of the Botswana Pula (BWP) and the US Dollar (USD) exchange rate and to identify the most plausible probability distribution from the skewed generalized t (SGT) family that can be used to model the log-returns of the daily BWP/USD exchange rates for the period January 2001 to December 2020. The SGT family is a highly versatile class of models that can capture the skewness and kleptokurticity that are inherent in financial time series. Four probability distributions are considered in this study: skewed t, skewed generalized error, generalized t and skewed generalized t. The maximum likelihood approach is used to estimate the parameters of each model. Model comparison and selection are based on the Akaike information criterion (AIC) and Bayesian information criterion (BIC). The results of the study show that the daily BWP/USD exchange rate series is nonnormal, negatively skewed heavy-tailed. It is also found that, based on the values of both the AIC and BIC, the model that gives the best fit to the data is the skewed t, which is closely followed by the skewed generalized error distribution, while the generalized t gives the worst fit. Keywords: Pula/US Dollar exchange rate, log returns, Generalized t distribution, Skewed generalized error distribution, Skewed generalized t distribution, Skewed t distribution, skewness, kurtosis, maximum likelihood
Highlights
IntroductionBotswana’s economy remains heavily dependent on mineral exports (especially the diamond subsector), despite government’s efforts to diversify the economy
Botswana’s economy remains heavily dependent on mineral exports, despite government’s efforts to diversify the economy
From the figure it is clear that there was some volatility in the trend of the Botswana Pula (BWP)/US Dollar (USD) exchange rate from about 2001 to 2005, followed by another bout of instability around 2008
Summary
Botswana’s economy remains heavily dependent on mineral exports (especially the diamond subsector), despite government’s efforts to diversify the economy. The US Dollar is one of the most important currencies in the basket of currencies to which the Botswana Pula is pegged For this reason, research on the Botswana Pula (BWP) and the US Dollar (USD) exchange rate using statistical methods, amongst others, by academics, regulators of financial institutions and investors has been gaining currency. The study by Sejoe et al (2020) uses cointegration approach to investigate the Purchasing Power Parity (PPP) theory of the Pula/Rand and Pula/US Dollar exchange in Botswana for the period of 1976-2016. We contribute to the literature on the BWP/USD exchange rate by determining a probability model that adequately describes the BWP/USD exchange rate. This is a key step in the construction of market risk assessment tools like the Value-at-Risk (VaR). A review of literature on statistical analysis and modelling of financial time series shows that an assumption that is most commonly made in financial economics theory and applications is that financial returns follow
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