An alternative approach could be to test for  breaks in the cointegrating relationship you are trying to estimate. Hansen and Johansen (1999), among others, propose a method based on recursively estimated eigenvalues. If structural breaks are present, you could use the Johansen, Mosconi and Nielsen (2000) methodology for testing cointegration in the presence of structural breaks.  JMULTI package, for example, implements both tests. 

Best,

Oana

References:

Johansen, S., Mosconi, R. and Nielsen, B. (2000), `Cointegration analysis in the presence of structural breaks in the deterministic trend', The Econometrics Journal 3(2), 216-249.

Hansen, H. and Johansen, S. (1999), `Some tests for parameter constancy in cointegrated var models', The Econometrics Journal 2(2), 306-333.

JMULTI can be downloaded from: http://www.jmulti.de/

Thank you, Rajesh! If a break the series - the observations will be too small a number to perform a good co-integration analysis. Probably, I will try the second option - non-linear cointegration test. I hope I will find the necessary papers.

An alternative approach could be to test for  breaks in the cointegrating relationship you are trying to estimate. Hansen and Johansen (1999), among others, propose a method based on recursively estimated eigenvalues. If structural breaks are present, you could use the Johansen, Mosconi and Nielsen (2000) methodology for testing cointegration in the presence of structural breaks.  JMULTI package, for example, implements both tests. 

Best,

Oana

References:

Johansen, S., Mosconi, R. and Nielsen, B. (2000), `Cointegration analysis in the presence of structural breaks in the deterministic trend', The Econometrics Journal 3(2), 216-249.

Hansen, H. and Johansen, S. (1999), `Some tests for parameter constancy in cointegrated var models', The Econometrics Journal 2(2), 306-333.

JMULTI can be downloaded from: http://www.jmulti.de/

Thank you, Oana! I have never worked with JMULTI package before. I will try it. 

Thank you, Rajesh! I downloaded JMULTI - it is really very helpful for time series analysis!

Thank you, Pandelis.

Regarding your question: The variables are I(1) before the structural break has been accounted for. I want to test whether this tendency continues when the breaks are accounted for. Due to the recent crisis there are breaks in most macro variables which I use.

As for the software, as far as I was able to see JMULTI suggested by Oana offers a possibility for a co-integration analysis in case of structural breaks. The only confusing thing is that the timing of the break varies between the different time series/variables. Is that means that I should use as many dummies as the number of the variables involved in the model?

Thank you, Pandelis! That is what I care about  - the number of observations and the degrees of freedom. Probably I will reduce the number of the variables if it is necessary.

I think several people already answered your initial question (1). 

In terms of question 2 - it depends a bit on the topic / what kind of data you are analysing.

I would recommend to run linear (johansen) cointegration test & depending on results (if you do NOT find any cointegration relationships) and this could be due to the different structural breaks. From there you can complement your analysis with Threshold cointegration methodologies. 

Thank you, Valeri! Actually the co-integration tests cleary identify the existence of more than 1 co-integrating realtions. I solved the problem by including structural break dummies as independent variables. They represent the break in the dependent variable. I think that a reliable output is produced in that way.