The effects of additive outliers on tests for unit roots and cointegration

The properties of the univariate Dickey-Fuller test and the Johansen test for the cointegrating rank when there exist additive outlying observations in the time series are examined. The analysis provides analytical as well as numerical evidence that additive outliers may produce spurious stationarity. Hence, the Dickey-Fuller test will reject a unit root too frequently, and the Johansen test will indicate too many cointegrating vectors. The results easily generalize to models with temporary change outliers. Through an empirical example, the analysis demonstrates how additive and temporary change outliers can be detected in practice, and it shows how dummy variables can be used to remove the influence of such extreme observations. A proper statistical procedure to detect outliers is necessary. Many statistical software packages for analyzing autoregressive integrating moving average models have built-in routines to detect outliers.