# I(1) and I(0) variables and cointegration in a trivariate system

I'm a bit confused regarding cointegration and I(1) and I(0) variables. I am testing the residual for cointegration in a regression where the nonstationary variables $x_1$, $x_2$ and $x_3$ are independent. If $x_1$ is I(1), must $x_2$ and $x_3$ also be I(1) for me to say that they are cointegrated?

• You'll need at least 2 of your 3 variables to be I(1). The third on can be I(0). What framework are you testing in? You can look at this answer to see if it helps you: stats.stackexchange.com/questions/130660/… Oct 21, 2016 at 10:31
• The idea with cointegration is that the stochastic trends cancel to produce stationary series. Therefore, in a system with three variables you will need at least 2 variables which are I(1) Oct 21, 2016 at 10:32
• @Plissken, why don't you turn that into an answer. Oct 24, 2016 at 18:31
• @RichardHardy, will do tomorrow. Oct 24, 2016 at 21:24
• @Plissken, tomorrow never came :) Mar 6, 2017 at 16:32