If we have multiple variables, we can explore the order of integration of linear combinations.
If two series have time trends, a linear combination of them could remove this.
\(Cov(x_{it},u_{it})=0\)
\(Cov (x_{is}, u_{it})=0)\)
This is stronger than contemporeous, all periods.
Shocks don’t affect future outcomes.
Sequential exogeneity: a bit looser than strict exogeneity. only holds when \(s\le t\).
So shocks can affect, but only in future.
Weak stationary processes can be decomposed to a deterministic and a stochastic component.