| dc.description.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 | en |
