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Hi,

I'm trying to build a model using 2 trend-stationary variables (my question is also valid for 1 trend-stationary and 1 unit root variables) and was wondering if the regular cointegration methods can be applied to this type of process? From what I understand, two variables are cointegrated if they share a common stochastic trend, however, could this also apply to variables that shares a deterministic trend? Moreover, does including a Trend in the cointegration equation (test) solves my problem?

Thanks.

Have a look at this document to help you out. Indeed, two trend stationary variables can be co-integrated. What happens, however, is that the cointegrating relationship purges the effect of the deterministic trend. If this was not the case, it would imply the presence of a trend in the cointegrating equation, making the latter I(1) rather than I(0).

https://www.fmf.uni-lj.si/finmath09/Cointegration.pdf

This is exactly what I was looking for. Thanks for sharing this document!

Follow up question.

Can anyone help me with the intuition of the different option provided for the different cointegration test (i.e. trend, no trend, constant...)

Is it better to test for cointegration using a trend in the equation when dealing with trend-stationary data. What factors would push me to use the trend instead of no trend in the cointegrating equation?

Thanks