I have a general question on VAR-methodology. In the case of asymmetric modelling I employ FGLS to exploit off diagonal covariance between residuals due to non-unique regressors between equations. Ok, now. What about the vectors that are by necessity zero, because they were never included? Should they be set to zero later in the Var-modelling or estimated as with restricted paramters (set to zero). This seems to me to take me from FGLS modelling to restricted-LS modelling. Is this even possible? So in a nutshell, which is preferred, to omit a parameter and set it to zero later, or to include it and restrict it to zero during estimation?
2$\begingroup$ What do you mean by vectors that are by necessity zero, because they were never included? Could you give an example? And how can you omit a parameter when setting up OLS or FGLS estimation? $\endgroup$– Richard HardyMar 6, 2015 at 10:33
$\begingroup$ Hi, and thanks for taking this on! Well, as you know in your VAR-universe we assume to be including "everything". But we really aren't. FGLS is equivalent to LS if regressors are identical, so we let lags vary between equations sometimes. Now, when constructing our companion matrix to check for stability, how do we format the individual A's (of equationwise estimated paramters) to get symmetry in this matrix? Just set the "un-estimated" paramters to zero? $\endgroup$– user70523Mar 6, 2015 at 12:08
1$\begingroup$ It would be helpful if you updated the original post with some equations illustrating what is what. $\endgroup$– Richard HardyMar 6, 2015 at 12:12
Since the "universe" is by definition limited anyway (p < infinity), I decided that whatever 1..p-lags, chosen for the individual equations represent are sufficient. Setting Everything else to zero might not be correct model selection wise, but i cannot upset the model mathematically.