Abstract:
The work presented in this thesis is done by both a simulation and empirical
study. Two series of data are simulated using the Generalized Autoregressive
Conditional Heteroskedastic (GARCH) model due to its ability to capture volatil-
ity and heteroskedasticity, which gives a guide to the empirical study. One main
proposition is made that if two time series follow GARCH(1,1), the two series
are cointegrated, a proposition rst proved using a simulation study. In the em-
pirical study, the U.S. dollar exchange rate and the interbank lending rate in
Kenya are analyzed. Co-integration and OLS are used; and the model parame-
ters tested for adequacy. The proposition in the simulation study is proved by a
case study of the Kenyan market. Both the exchange and lending rates returned
non-stationarity in all the tests. Di erencing is applied to attain stationarity.
Co-integrating factor is then estimated to be -0.490747, with its residuals being
stationary. Relatively same R2 and adjusted R2 values indicates adequacy of the
model which ascertains the proposition. Granger causality tests were as well done
and only the exchange rate granger caused interbank lending rate. This can be
explained by the instability in the exchange market. A linear Error Correction
Model (ECM) is also tted and there is evidence that a short-term relationship
exists between the lending and the exchange rates. A high threshold value exists
at the second lag, an indication of simple smoothing in the data. The residual de-
viance is greater than the degrees of freedom con rming that the model perfectly
t to the data, supported by the high R2 value of 0.9308. It is recommended
that a close track of exchange rates may lead to prediction of interbank lending
rate movements. Further study should be conducted on tail clustering analysis,
as well as on the factors in
uencing exchange rate movements and analysis of
tail clustering. Also, a similar study should be undertaken with a combination
of Auto Regressive Moving Average Process (ARMA) and GARCH models to
capture both conditional variance and conditional expection properties.
