Hi Nino,
As per my understanding, to recover the companion-form matrix from the estimation using the "varm" function in the Econometrics Toolbox, you can have direct access the estimated var model's coefficient matrix. The companion-form matrix is a rearrangement of the coefficient matrix where the lagged endogenous variables are stacked in a vertical manner. Here is a code snippet for your reference
model = varm(2, 2); % 2 lags and 2 endogenous variables
estModel = estimate(model, <input_data>);
% extract coefficient matrix for the first lag
coefficientMatrix = estModel.AR{1};
companionMatrix = [coefficientMatrix' eye(size(coefficientMatrix, 1) * (model.NumSeries - 1))];
In the approach demonstrated above, "estModel.AR{1}" returns the coefficient matrix for the first lag. The companion-form matrix is then constructed by stacking the transpose of the coefficient matrix vertically, followed by an identity matrix multiplied by the number of endogenous variables minus one.
I hope this helps.
