Many econometrics papers provide the parameters used in their VAR model. If I notate my VAR model as
$$z_{t+1} = c + B z_{t} + \Sigma \epsilon_{t+1}$$
where $\epsilon \sim N(0, I)$, then I need to know $c, B$ and $\Sigma$.
The paper
arno.uvt.nl/show.cgi?fid=113711
I was looking at provides $B$ and the $\Sigma' \Sigma$ which they describe as the "cross-correlations of the innovations with monthly standard deviations on the diagonal".
When trying to reproduce their model, I think that I should not be using their provided $\Sigma' \Sigma$ as $\Sigma$, but am unsure about how I could get $\Sigma$. Additionally, all the papers I've seen using a VAR don't provide the $c$, so I assume that it is a vector of 0's.
I was hoping that someone could clarify how one might get a value of $\Sigma$ (the covariance matrix) from a research paper and whether my assumption about $c$ is incorrect or not.
They run OLS regressions; it would be odd if the axis intercept ($c$) would happen to be $0$ for all variables. But as they are focussing on to autogregressions of the variable vector, I suppose, they simply do not consider the intercept interesting enough to put it in the estimation results.
I agree that it is somewhat unconventional that they give $\Sigma'\Sigma$ but not $\Sigma$. Then again, already the very presence of the $\Sigma$ in the regression equation is unconventional. Normally, VARs do not multiply other factors to random error terms (see here), but this is, of course, a question of what kind of errors you assume for your model.
Not having red the full paper, I did not find any explanation for why they did it this way. $\Sigma$ appears to be the covariance matrix over the time series of the variables. They have the model from here , chapter 4 (note that in this work, the previous models use other VAR models with simple error terms without $\Sigma$).
I suppose, you could compute $\Sigma$ (and $\Sigma'\Sigma$ for that matter) if you had access to the time series.