Economic applications of co-integration in time series (A Case Study of the Kenyan Exchange and Interest Rates) h

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.