The question is generally about what test equation should I use for testing the unit root of a series with two, say, intercept breaks. But I have specific questions.
The whole procedure is as follows, but was really not sure if it's theoretically sound....(I am not a econometric student)
- I inspected the graph and can see two breaking points.
- I used EViews to run a normal ADF test, using SC to choose lag length and, as expected, I failed to reject Null.
- I used Bai-perron test (L + 1 VS. L) to sequentially determine intercept-breaking dates on the same ADF equation as step 2, giving me two breaking points.
- I constructed two dummies based on the estimated dates.
- I included these two dummies into the ADF equation in step 2 and estimated it again, rejecting the null. I then conclude no unit roots.
Two main reasons or specific questions lead me to concern:
- What should be the input test equation for Bai-perroon sequential test? Should I put a parsimonious AR(1) or the AR(p) model EViews estimated, given there are structural breaks.
- I do have a basic understanding that, for a single break series, the Perron test nests hypotheses into one equation and tests a null hypothesis of random walk with a break against a stationary series with a break, and it also includes a pulse dummy into the equation. So, in my step 5, should I also include two pulse dummies into the ADF equation given that I have two breaks estimated? Or I just use the two dummies as controls in the ADF test ........I think this may be a dumb question....but I am really struggling.
If you have a better way to test the unit root of a series with multiple breaks, please advise!!
(no trend in the series)