Engle-Granger cointegration testing with a structural break

Question

I have two series of daily close prices for UN and UL from 01/02/2002 to 12/31/2002. Both are for Unilever Co. When I conduct the Engle-Granger cointegration test, the MacKinnon $p$-value is high, meaning no cointegrating relationship. However, just by looking at a graph of the two series for that particular period, there appears to be a strong cointegrating relationship.

Does this happen because the UN series crosses over the UL series, causing the residuals from OLS on prices to appear nonstationary?

Below are graphs of the UN and UL close prices and the residual plot.

Answer 1

The residual series indeed seems to have a structural break (or a gradual structural change) around July 2007, which makes it appear nonstationary. The unconditional mean of the residuals before July 2007 clearly differs from the unconditional mean after July 2007. This can induce a unit root test as used in the Engle-Granger procedure to find presence of a unit root even though the true cause is a structural break/change. I can thus only support your guess.

What you could do is allow for a structural break (or a gradual structural change) around July 2007 in the Engle-Granger test. I am not sure whether simply including a dummy variable in the first stage regression would work alright (that is, whether the null distribution of the parameter of interest in the test regression would remain intact) but perhaps there is some related literature elaborating on this question. Alternatively, you could just ignore the period around the structural change and do two separate tests for the early and the late periods.