[R] Restrict a SVAR A-Model on Matrix A and Variance-Covariance-Matrix

[chili]

Hello folks!

I'm using R-Package {vars} and I'm trying to estimate an A-Model.

I have serious problems regarding the restrictions.

1) My A-Matrix needs (!) to have the following form:

# 1 NA  NA  NA  
# 0  1  NA  NA
# 0  0   1  NA
# 0  0   0   1

That is done in R by:

A_Matrix <- diag(4)   # main diagonal = 4 restrictions
A_Matrix [1, 2] <- NA #
A_Matrix [1, 3] <- NA #
A_Matrix [1, 4] <- NA #
A_Matrix [2, 3] <- NA #
A_Matrix [2, 4] <- NA #
A_Matrix [3, 4] <- NA # off diagonal = 6 restrictions


2) The Variance-Covariance-Matrix of the structural residuals needs (!) to
be looking like:

#
# var(X1)        0               0             0
#       0        var(X2)         0             0
#       0          0           var(X3)         0
#       0          0               0       var(X4)

Since cov(xy)=cov(yx) there are 6 more restrictions.
So in total I would have 4+6+6=16 restrictions. The SVAR would be just
identified.

My problem is that I don't know how to implement this
Variance-Covariance-Matrix within R and {vars}.

My Code so far is:

# Prediction SVAR - A-Model (B-Matrix = NULL)
# restrictions:
# 1) Amat = A_Matrix
# 2) ????

VAR.est <- VAR(data.ts, p = 4, type = "none")
SVAR.A.est <- SVAR(x=VAR.est, estmethod = "direct", Amat = A_Matrix , 
                   Bmat = NULL, hessian = TRUE, lrtest = TRUE)

#--------------------------------------------------------------------

I know, that {vars} restrict the Variance-Covariance-Matrix by default to an
identity-matrix but I wondered if I can't restrict it by myself since the
way I need (!) to do that is quite common.

Thank you for any comments. I'm quite desperate right now :/



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