Exchange market pressure in South Africa and Kenya: An analysis using parametric and non-parametric extreme value theory

Abstract

Orientation: Exchange market pressure (EMP) is the selling pressure of domestic currency or excess demand needed for foreign currency. Research purpose: The purpose of this study was to analyse EMP using extreme value theory (EVT) and to compare two commonly used EVT methods. Motivation for the study: To determine whether the EMP of two African countries can be modelled with EVT, and if so, which method would be best suited. To determine periods of extreme pressure or currency crisis by using these methods. Lastly, to study the individual components of the EMP index during these periods of stress of crises. Research design/approach and method: The monthly data of the three components of the EMP index for two African countries (Republic of South Africa [RSA] and Kenya) were studied for a period of 19 years (1999–2017). The data were modelled using the generalised Pareto distribution (GPD) with the peak over threshold (POT) method using maximum likelihood estimation. Moreover, the data were also modelled using the non-parametric Hill estimate. Appropriate estimated and empirical quantiles are reported in order to determine periods of extreme pressure or crises. The components of the EMP RSA data set were modelled with appropriate autoregressive moving averages and/or autoregressive conditional heteroscedasticity/generalised autoregressive conditional heteroscedasticity (ARMA/ARCH/GARCH) processes to ensure independent and identically distributed variables. Main findings: Reliable and accurate estimates were obtained for the scale and shape parameter using the GPD POT method for both countries. Positive shape parameters confirmed generalised extreme value distributions with heavy tails of the Frechet type. Similarly, accurate and reliable shape estimates were computed using the non-parametric Hill estimator for both countries. Practical/managerial implications: The GPD POT method more closely reflected estimates to the empirical qauntiles compared to the Hill method. It is feasible to model the EMP data of two African countries with EVT using both POT estimation methods. However, the GPD method using maximum likelihood estimation was more accurate compared to the non-parametric Hill estimate. Contribution/value-add: It is feasible to model the EMP data of two African countries using EVT using both POT methods. As a consequence periods of extreme pressure could be identified. Therefore the individual components of the EMP at those periods of extreme pressure could be studied more closely.

Keywords

• exchange market pressure
• extreme value theory
• generalised Pareto distribution
• peak over threshold
• Hill estimate
• extreme pressure
• currency crisis