I have applied the Johansen et al. (2000) cointegration test with a level shift, but his paper is very complicated at this stage for me to understand fully. I want to know once a level shift is considered, what will be the mathematical form (model) of Johansen's cointegration test and its corresponding trace statistic? If you can understand his paper, please leave the equations in the comments.
Thanks in advance.
Sincerely
This is a good question.
Answers to this question can be found in
B. Sjoe, Testing for unit roots and cointegration, 2008:
https://www.iei.liu.se/nek/ekonometrisk-teori-7-5-hp-730a07/labbar/1.233753/dfdistab7b.pdf
For the mathematical formulation of Johansen's trace test, see Remark 9, p. 15. The Johansen cointegration test is explained in detail in Section 6, starting on p. 13.
The equations in Sjoe (2008, remark 9) remain relevant for the Johansen et al. (2000) approach to structural breaks. Because of the structural break(s), the computation of the eigenvalues will differ in detail from Johansen (1995) and the statistical properties of the test statistics also differ. Section 5 of Hong Li & Vince Daly (2009) "Testing the Balanced Growth ..." Empirical Economics 37:185-200 employs Johansen (2000) and provides some equations.
Dear Prof. Daly,
Thanks for the information and reference.
Although, I learned the Johansen (2000) model, this will further add to my knowledge of the same.
Thanks,
Najibullah
Dear Prof. Daly,
Thanks for the information and reference.
Although I have eventually learned the Johansen (2000) model, this will further add to my knowledge of the topic.
Thanks,
Najibullah
You can see Cats2 for Rats. In the manual you can find the mathematical expression.
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