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)

Main article: Vector autoregression

where each is a vector of length k and each is a k × k matrix.

Large matrix notation

Equation by regression notation

Rewriting the y variables one to one gives:

Concise matrix notation

One can rewrite a VAR(p) with k variables in a general way which includes T+1 observations through

where:

and

One can then solve for the coefficient matrix B (e.g. using an ordinary least squares estimation of ).

References

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