Modelling the Botswana Pula/Us Dollar exchange rate using the Skewed generalized t (SGT) distributions
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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
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