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
- Lütkepohl, Helmut (2005). New Introduction to Multiple Time Series Analysis. Berlin: Springer. ISBN 3540401725.
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