Hi there,
the SVAR analysis is a powerful tool and Jack's SVAR package already in
it's present state is magnificent!
At the moment I'm working through it step by step. My ultimate goal is
to perform a 'Structural vector autoregressions with
nonnormal residuals' by Lütkepohl (see attached file). Unfortunately his
examples are SVECMs which makes the stuff even more complicated.
However, while learning from the 'SVAR code' and with Lütkepohl's book
'New Introduction to Multiple Time Series Analysis' I came across the
following questions:
a) In his book on page 367 (section 9.1.3) the Rd matrix (following the
notation of Jack) seems to me wrong.
b) Is it in order to use 'abs(nullspace(R))~R'invpd(R*R')*d' instead of
the things done in imp2exp (and btw. exp stands for expansion, or, and
imp for ?)
<hansl>
nulldata 10
include SVAR.gfn
#example
matrix
R_Luedkepohl={1,0,0,0,0,0,0,0,0;0,0,1,0,0,0,0,0,0;0,0,0,0,1,0,0,0,0;0,0,0,0,0,1,0,0,0;0,1,0,0,0,0,1,0,0;0,0,0,0,0,0,0,0,1}
eval R_Luedkepohl
matrix
R={1,0,0,0,0,0,0,0,0;0,0,1,0,0,0,0,0,0;0,0,0,0,1,0,0,0,0;0,0,0,0,0,1,0,0,0;0,0,0,0,0,0,1,0,0;0,0,0,0,0,0,0,0,1}
eval R
matrix R_orth={0,0,0;1,0,0;0,0,0;0,1,0;0,0,0;0,0,0;0,0,0;0,0,1;0,0,0}
eval R_orth
eval R*R_orth
matrix d ={1;0;1;0;0;1}
matrix Rd=R~d
eval imp2exp(Rd)
matrix s = R'invpd(R*R')*d
eval abs(nullspace(R))~s
<hansl>
Cheers
Leon