Muhamad,

if your data have a structural break (SB), then they are most likely nonstationary. A fair question to ask is if *apart from the structural break* is there any signature of nonstationarity. In this case you should be able to detect when and what kind of structural break occurred and then use some data transformation to greatly reduce the effect of the SB e.g. detrend the data with different detrending models before and after the SB. Of course, if you are not sure about the type of SB then this will not help much. You can think of many suboptimal alternatives e.g. divide your data at the SB and test each part separately (with data transformation if necessary); you may fit models to each portion of data and compare the models; you may compute the autocorrelation function to each portion of the data (separated by the SB) and compare the results...

Hey,

I'm really no expert in this field but I think a colleague of mine did some research on it:

https://www.researchgate.net/profile/Andreas_Dechert

Unfortunately, he is not in the academic field anymore so I cannot ask him. But perhaps it helps.

Kind regards,

Florian

If you know or you suspect the moment where the structural break happened, you can do as Sophia suggests: test if there's actually an structural break or not, for example, using the Chow test for structural change. You can also try to adjust a linear regression model using a time trend and dummy variables, something like this:

Y -> Your series

B -> Dummy variaable: 1 for observations before the shock, 0 for observations after the shock.

A -> Dummy variable. 0 for observations before the shock, 1 for observations after the shock.

T -> Time trend.

You estimate the model: Y = b(1)*A + b(2)*B + b(3)*A*T + b(4)*B*T + Ui

Then you test (separately) the following hypothesis: b(1)=b(2) and b(3)=b(4).

If you reject that b(1)=b(2) OR b(3)=b(4), then you have an structural change.

If the test confirms the existence of a break, do as Luís Antonio says: divide your sample in two sub-samples (one before the break, the other one after the break) and test for stationarity separately in each of the two sub-samples.

Dear Muhamad, one of the most recently developed (linear) unit root testing technique is the one proposed by Carrion-i-Silvestre et al. (2009), which can identify up to five break points in the series by using a quasi-GLS algorithm that minimises the residual sum of squares.Given the time span of your sample, this test would allow you to capture more possible breaks in the series than those typically tested for by older unit root tests (e.g., ADF, Ng-Perron, Z-A, L-P, etc.), and hence place greater confidence in the unit root test results (see full reference below). For a good application of the Carrion-i-Silvestre et al. (2009) unit root test see my paper (downloadable from my research gate page) titled ‘Revisiting the Environmental Kuznets Curve Hypothesis in a Tourism Development Context’ by De Vita Glauco et al. (2015), published in Environmental Science and Pollution Research.

I hope this helps and good luck with your research. 

Reference: Carrion-i-Silvestre JL, Kim D, Perron P. 2009. GLS-based unit root tests with multiple structural breaks under both the null and the alternative hypotheses. Econometric Theory 25(6): 1754–1792.