Structural breaks can sometimes be a huge hassle to deal with when you are trying to investigate the long run relationship between the variables by running standard cointegration tests such as Engle-Granger or the standard Johansen test.
Now, when the structural breaks are present, one solution is the residual-based cointegration test proposed by Gregory and Hansen (1996). The relevant R programs and example can be found on website of Bruce E. Hansen by clicking here. Note that p is number of variables and r is number of cointegrating rank being tested
The test proposed by Johansen et al. (2000) appears to be another solution. The relevant R program for computing the critical values can be found at Dave Giles’ website here. (In the program, remember to set the correct breakpoint proportion and the value of q!!)
To do the Johansen et al. (2000) test, it can be decomposed into the following steps:
Step1: Identify the structural breaks.
Step2: incorporate the date dummy (D2), trend*dummy interaction term(D2*@trend), as well as the shift indicator dummy(I2) as exogenous variables into the original VAR. In Dave Giles example, the variables he adds are D2(-2), I2(-1), trend*D2(-2), and I2.
step 3: construct the usual Johansen trace statistics
(How to calculate the trace statistics? See this paper here )
The asymptotic critical values depend on the proportion of the way through the sample that the break occurs (λ = 0.44 in our case); and on (p – r), where p is the number of variables under test p = 2, here), and r is the cointegrating rank being tested. So, for us, r = 0, 1. Unlike Gregory-Hansen (1996) test, the Johansen et al. (2000) test can be modified to allow for two structural breaks.
I downloaded the EViews workfile, which is available here
Now Time for some sleep before tomorrow’s work….Zzzzzzz