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?
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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: http://stats.stackexchange.com/questions/130660/test-for-cointegration-between-two-time-series-using-engle-granger-two-step-meth/130762#130762 – Plissken Oct 21 '16 at 10:31
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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) – Plissken Oct 21 '16 at 10:32
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1@Plissken, why don't you turn that into an answer. – Richard Hardy Oct 24 '16 at 18:31
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@RichardHardy, will do tomorrow. – Plissken Oct 24 '16 at 21:24
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1@Plissken, tomorrow never came :) – Richard Hardy Mar 06 '17 at 16:32