Estimation of a Co-integration Model Using Ordinary Least Squares (A Simulation Study)

Rotich Titus Kipkoech, Orwa Otieno George, Mung'atu Kyalo Joseph

Abstract: Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models are usually used to analyse time series data with high volatility clustering. In this paper, it is proposed that if two time series follow GARCH (1, 1), the two series are cointegrated and accordingly, we simulate data using the GARCH model which are used to prove this proposition. The choice of the simulation models is based on its ability to capture volatility and heteroskedasticity. Co-integration and Ordinary Least Squares methods are used; and the model parameters investigated for adequacy. Results from Augmented Dickey Fuller (ADF), Phillips Perron (PP) and Kwiatkowski Philips Schmidt Shin (KPSS) tests indicates stationarity in the data as expected. The Engle-Granger two-step method for testing co-integration is used. A linear co-integration model is estimated with coefficient of co-integration, l, being 1.60477. Residuals from the fitted linear model are also stationary. A high R2 value of 0.8633 is obtained which indicates adequacy of the model. This completes the proof and we conclude that the proposition holds; and also that co-integration models can be used to analyse time series data with high volatility and heteroskedasticity. Such data include share prices and exchange rates. It is recommended that a similar study be undertaken but with a combination of Auto Regressive Moving Average Process (ARMA) and GARCH models

Keywords: Co-integration, Ordinary Least Squares, Simulation, GARCH