General matrix notation of a VAR(p)


This page shows the details for different matrix notations of a vector autoregression process with k variables.

Var(''p'')

where each is a vector of length k and each is a k × k matrix.
What are the assumptions on the noise?

Large matrix notation

Equation by regression notation

Rewriting the y variables one to one gives:

Concise matrix notation

One can rewrite a VAR with k variables in a general way which includes T+1 observations through
where:
and
One can then solve for the coefficient matrix B.