Exchange market pressure in South Africa and Kenya : an analysis using extreme value theory
INTRODUCTION: Extreme value theory (EVT) is a branch of probability statistics applicable to financial data distributed with heavy tails where the distribution is stationary, independent and identically distributed. EVT is important for modelling situations that are rare in frequency but large in magnitude in terms of losses, depreciation or pressure. It is useful in conditions where a currency experiences extreme pressure or crises. Exchange market pressure (EMP) is the selling pressure of domestic currency or excess demand needed for foreign currency and composed of a weighted average of three components (rate-in-change in exchange rate, rate-in-change in interest rate and rate-in-change in reserves-to-narrow money). The objective of EMP is to determine periods of "extreme pressure" or currency crises (periods of successive stress). EMP using EVT has never been explored in African countries. Moreover, a comparison of two peak over threshold methods used in EVT (Generalised Pareto Distribution and Hill estimate) is studied and compared to empirical quantiles for measurement accuracy. In doing so, periods of extreme pressure or crises can be identified. Subsequently, the causes of these unwanted situations can be identified and monitored. METHODOLOGY: The monthly data of the three components of the EM P index for two African countries (RSA and Kenya) were studied for a period of 19 years (1999-2017). Data was first studied to ensure stationarity and modelled with appropriate ARMA and/or ARCH/GARCH processes to ensure no heteroscedasticity. Once all assumptions were met for further analyses, the EMP index was calculated. Subsequently, the data was modelled using the Generalised Pareto Distribution (GPO) with the Peak over Threshold (POT) method using maximum likelihood estimation. Moreover, the data was also modelled using the nonparametric Hill estimate. Appropriate estimated and empirical quantiles are reported in order to determine periods of extreme pressure or crises. Data analysis was performed in Microsoft Excel (Microsoft, Redmont, United States) and R studio (CRAN, R Core Team, 2017) with associated packages. RESULTS: The EMP index for both countries revealed stationarity but non-normality. The components of the EMP SA data-set were modelled with appropriate ARMA and/or ARCH/GARCH processes to ensure independent and identically distributed variables. Reliable and accurate estimates were obtained for the scale and shape parameter using the GPO POT method for both countries. Positive shape parameters confirmed generalised extreme value distributions with heavy tails of the Frechet type. Diagnostic plots revealed a good fit for the model. Similarly, accurate and reliable shape estimates were computed using the non-parametric Hill estimator for both countries. Estimated quantiles are provided using both methods. The GPO POT method more closely reflected estimates to the empirical qauntiles compared to the Hill method, especially at higher quantiles. Using, the 95th and 99th quantiles, periods of extreme pressure for each country is identified. In doing so, the respective components of the EMP index is evaluated against the backdrop of periods of extreme pressure or crises. Eight and ten periods of extreme pressure was identified for South Africa and Kenya respectively with no periods of currency crises (p=0.05). All three components of the EMP index played an individual role in the depreciative stress at different periods of pressure. CONCLUSION: It is feasible to model the EMP data of two African countries with EVT using both peak over threshold estimation methods. However, the Generalised Pareto Distribution's method using maximum likelihood estimation was more accurate compared to the non-parametric, Hill estimate, especially at the 99th or higher percentiles.