Estimation of a Co-integration Model Using Ordinary Least Squares (A Case Study of the Kenyan Market)

From a previous study on co-integration, it has been proposed that if two series follow a Generalized Auto-regressive Conditional Heteroskedasticity (GARCH (1, 1)) model, then the two series are co-integrated. However, the proposition was carefully proved using a simulation study. In this paper, a proof of this proposition is presented by applying a case study of the Kenyan market. The dollar exchange and Interbank lending rates in Kenya are analyzed. The procedure described in the simulation study is carefully followed, and consequently all the tests and justifications given follow. Unit root tests (Augmented Dickey Fuller (ADF), Phillips Perron (PP) and Kwiatkowski Philips Schmidt Shin (KPSS)) on the data indicates non-stationarity. Differencing is applied to attain stationarity. Co-integrating factor is then estimated to be -0.490747, with its residuals being stationary. elatively same R2 and adjusted R2 values indicates adequacy of the model. This ascertains the proposition; and also that co-integration models can be used to analyse time series data with high volatility and heteroskedasticity. It is recommended that a similar study be undertaken with a combination of Auto Regressive Moving Average Process (ARMA) and GARCH models to capture both conditional variance and conditional expection properties