# Unit root test specification with a structural break

I am puzzled as to what specification I should include in my unit root tests of the following data: .

I will use ADF, KPSS and ZA tests. I can see there is a break in trend at observation 9. However, for the former two tests, especially for ADF, I do not know what to choose as a final specification.

• You can perform unit root (or trend stationarity) test in the presence of break. There are plethora of such tests. You might want to read section 5 of following review article to choose the one sws1.bu.edu/perron/papers/dealing.pdf. I think most of them are readily available in R. – Khashaa Dec 28 '14 at 6:54
• Check this page people.bu.edu/perron he has many methods for dealing with unit roots and structural breaks (both level and trend breaks), plus there is some code in Matlab for testing that... – arroba Jul 14 '15 at 14:20

ADF test is pointless in this case. It's not going to give you a meaningful result.

The trend stationary is not going to detect this "break". All it looks at is whether the end is far enough from the start. The same with the drift: your start is not far from end in comparison to how much it went down first.

I bet you suspect that there was a trend down, then up. So, you have to test this hypothesis. For instance, run ADF test on first and second halves separately to establish there is a trend. Then run Chow test to detect the break. This will support the "obvious" graphical evidence of what I just wrote. Basically, you don't need any tests in this case.

• Even if your ADF test shows no unit root in sample 1 and 2 respectively this does not mean that you can reject the unit root hypothesis for the entire sample. The correct approach would be to use a unit root test which can accommodate structural breaks. That being said this sample is probably to small to give any reasonable results. – Plissken Dec 28 '14 at 12:35

On the ADF test, there is a "rule of thumb" to selection of $p_{\text{max}}$ (highest $p$).

The $p_{\text{max}}$ is given as $12\cdot \left(\frac{T}{100}\right)^{0.25}$, by Schwert (1989), try this and move downwards from this $p$, and check for serial correlation of the residuals until you're happy with your results.

• Dear @user21240, many thanks for your answer. I am looking for your views about the specification for the unit root tests. should I include trend in the final specification? – mr.rox May 4 '13 at 14:59
• From the plot, it doesn't really look like a trend, but there is a constant which should be included in the test, that is case II. – fredrikhs May 5 '13 at 16:56
• Many thanks @user21240, do you think I should include a trend break dummy in the regression model as there seems to be a break at time 9? – mr.rox May 7 '13 at 13:17