This page just shows the details for different matrix notations of a VAR(p)

Vector autoregression

Vector autoregression is a statistical model used to capture the linear interdependencies among multiple time series. VAR models generalize the univariate autoregression models. All the variables in a VAR are treated symmetrically; each variable has an equation explaining its evolution based on...

 process with k variables.

Var(p)

Where each is a k x 1 vector and each is a k x k matrix.

Large matrix notation

Equation by equation 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

Ordinary least squares

In statistics, ordinary least squares or linear least squares is a method for estimating the unknown parameters in a linear regression model. This method minimizes the sum of squared vertical distances between the observed responses in the dataset and the responses predicted by the linear...

estimation of )