Time Series Analysis: Method and Substance Introductory Workshop on Time Series Analysis

Advanced Topics: Cointegration

• Two time series are cointegrated if:
• They are integrated of the same order, I(d)
• There exists a linear combination of the two variables that is stationary (I(0)).
• Most of the cointegration literature focuses on the case in which each variable has a single unit root (I(1)).
• Tests by Engle-Granger involve 1) unit root tests, 2) estimating an OLS model on the I(1) variables, 3) saving residuals, and 4) testing whether the first order autocorrelation coefficient has a unit root (they are not cointegrated) or not (they are cointegrated), Δet = a1et-1 + εt.