# Applying VECM (mean reversion) cointegration to three different series

Specifically, I'm looking at 3 different commodity futures prices. I want to test that each is unit root and that they are cointegrated. Next, I'd like to apply a model to them to test if they (or a combination of them) are mean reverting.

What I want to see is the evolution of a margin of 3 prices. X=price 1 Y=price 2 Z=price 3 M=Margin

M = (X+Y)*a - Z

first I was going to ADF to test each series for unit roots.

Is it possible to test M directly for mean reversion? I'd like to be able to see when M is too high/low from historic margins and price. Could someone please help??

You could as an informal test run a unit root test on your $M$ series.
More formally, it depends on whether $a$ is estimated from the data or chosen by you based on external theory/information:
• If $a$ it is estimated form the data, then $M$ is measured with imprecision, and hence the test should take this into account as finite-sample correction. This is what the Philips Ouliaris cointegration test actually does.
• On the other side, if $a$ is chosen by you, you can run the test directly.