Application of GARCH to Model the KESIUS$ Foreign Exchange Rates Returns

Abstract

The USA dollar (US$) is the most prominent currency around the world for transactions and also as foreign reserves for many Central Banks, for example in 2006, Central Bank of Kenya had 52% of its foreign reserves in US dollar currency. The change in the strength of the US$ relative to Kenya shilling (KES) has an impact on many socioeconomic sectors in Kenya. This research focuses on KES against US$ daily exchange rate returns from 2nd November 2004 to 315t December 20 IO. The Box-Jenkins models for time series assume homoscedasticity in the time series, however the returns exhibits stylized facts which can only be well modeled using conditional heteroscedacity-type of models. This project considers the application of Autoregressive Integrated Moving Average (ARIMA) models on the exchange rate. The ARIMA (4,1,2) model was fitted and its residuals exhibited volatility clustering and hence Generalized Auto regression Conditional Heteroscedacity (GARCH) was applied to address these characteristics. A quasi maximum likelihood estimation procedure was used and the estimators given. It was found that the returns are leptokurtic and have fat tails. GARCH(1, I) were fitted on the returns and was found to fit the returns well and its residuals found to be white noise and homoscedastic. The one day ahead forecasting are quite good implying that it could be used for future prediction on the volatilities of the returns. IV