ABSTRACT. An analysis of quarterly real gross domestic product (GDP) growth rates in South Africa for the period 1960 to 2011 is done using an autoregressive moving average-exponential generalized autoregressive conditional heteroskedasticity (ARMA-EGARCH) model and the extreme value theory (EVT) modeling framework. A two stage approach is used. An estimate of an ARMA-EGARCH model is done in stage one. In stage two, the EVT framework is applied to the lower tail of the distribution of the real GDP growth rates. The advantage of this approach lies in its ability to capture conditional heteroskedasticity in the data through the ARMAEGARCH model, while at the same time modeling the extreme tail behavior through the EVT framework. Empirical results show existence of volatility persistence and excess kurtosis in the real GDP growth rates. The generalized extreme value distribution (GEVD) produces more accurate estimates of extreme tails than a pure ARMA-EGARCH model. Modeling of extreme negative growth rates is very important for economic planners and the use of EVT-based approaches gives accurate estimates of extreme growth rates. pp. 81–94
JEL codes: D92, N1, O4

Keywords: tail quantiles, generalized extreme value distribution, GDP, EGARCH

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School of Statistics and Actuarial Science
University of the Witwatersrand

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