I checked the cointegration between two variables X and Y using Engel Granger's method and it came not co - integrated. Now I wish to divide x into x1 and x2 and y into y1 and y2 and again check for co - integration, do I need to check for stationarity of x1 and x2 (I already know x is non - stationary). But my x1 is coming stationary. Can I apply co integration after breaking the series? Please help.
How about using ARDL where you do not have to worry about integration issues of unity or zero. That will save your time.
We have already noted that not all variables can cointegrate. Splitting them may not yield a linear combination which is stationary. That said, you may have a situation in which all you can talk about is the short dynamics. In that cas, you can simply present your results using only first- differenced series. Your t- statistics are all meaningful becauseYou can also do ARDL since augmented Dickey-Fuller test may yield mixed results As I noted earlier, the ARDL estimator yields consistent results regardless of degree of integration. If the. FPSS iis larger than the table or upper critical value, the one can reject the null hypothesis of no cointegration. Then, we can conclude that there is cointegration. I hope this helps!
as suggested using ARDL maight be good option, especially splitting the variables into two subsamples, since all traditional unit root tests require large samples. Also, you have to take into account of break(s), it there is any , in the data. Finally, because of the established drawbacks of ADF test, I suggest to use NG-Perron unit root test.
Many suggestions have been given so to conclude this issue, do ARDL since it is good with small samples,it is applicable whether one has l(0), i(1) or fractions integrationed variables or not. You can supplement it with ADF. Perron test is also okay but really with ARDL, you should care about these supplemental tests. This is my ARDL is good.
I beg to disagree with some aspect of Arthur's suggestion concerning Johansen estimator.The Johansen technique is a system estimator, therefore, it has a greater chance of producing wrong results with any misspecification -- see Arize, Osang and Slottje (2008:37 ) in the International Review of Economics & Finance 2008. In addition, one should bear in mind that the one question asked concerns the point "i have two variables X and Y. "
I believe his question says one is coming out stationary and the other is non-stationary, then it follows to attempt normalizing on the stationary one and doing ARDL.
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