Multivariate time series

Multiple time series


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.


Contemporaneous exogeneity


Strict exogeneity

\(Cov (x_{is}, u_{it})=0)\)

This is stronger than contemporeous, all periods.

Shocks don’t affect future outcomes.

Sequential exogeneity

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.