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)

  1. I inspected the graph and can see two breaking points.
  2. I used EViews to run a normal ADF test, using SC to choose lag length and, as expected, I failed to reject Null.
  3. 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.
  4. I constructed two dummies based on the estimated dates.
  5. 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:

  1. 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.
  2. 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)

Thank you!!

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