Update: imp2exp: implicit to explicit :-) Pindar <pindar777(a)gmail.com&gt;: > 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 > <cesifo1_wp1651.pdf>

Update 2: There is a small bug in the SVAR package when writing the free parameters into the model (in the last step). Just run the hansl snippet.

I found 2 typos in the help pdf for the SVAR package, and the references are only "?" (a bibtex problem): 1. p10 under 2.4: it's $\frac { n(n-1) }{ 2 } $ restrictions 2. p. 21 under SVAR.cumulate: Stores into the model

>> a) In his book on page 367 (section 9.1.3) the Rd matrix (following the >> notation of Jack) seems to me wrong.

Am 09.11.2012 12:36, schrieb Riccardo (Jack) Lucchetti: > On Sat, 3 Nov 2012, Pindar wrote: > >> Update 2: >> There is a small bug in the SVAR package when writing the free >> parameters into the model (in the last step). >> Just run the hansl snippet. > > Not really a bug. The vector containing the unrestricted parameters > only is implicitly defined by the relationship (allow me to use LaTeX) > \[ > \theta = S \gamma + s > \] > where $\theta$ contains the total vector of parameters and $\gamma$ > the unrestricted ones. Now, in the SVAR package the matrix $S$ is > automatically defined via the constraint matrices in implicit form $R > \theta = d$ through the relationships $RS = 0$ and $Rs = d$. This > means that $S$ is defined up to post-multiplication by an arbitrary > invertible matrix. As a consequence, you can change the ordering of > the columns of $S$ in any way you want, but of course this will > affect the ordering of the elements of $\gamma$; this fact, however, > is observationally inconsequential. > Thanks for that explanation. In terms of estimating the SVAR a have another question: Why is it this equation ll=-0.5*(tr(inv(C*C')*Sigma)-ln(det*(inv(C*C')*))) that works and not this equation ll=-0.5*(tr(inv(C*C')*Sigma)-ln(*det(C*C')*)) which one finds in Luetkepohl on p. 372 ?

Btw, if one wants to estimate the C- and VAR- parameters jointly (not using the concentrated ll) should it be possible with numeric derivatives? I didn't succeed with the VAR in MLE form with 'deriv' statement... Just this: <hansl> matrix A=vec(zeros(n,p*n)) mle llm=-n*T/2*ln(2*$pi)-T/2*ln(det(vcv))-0.5*tr(vcv*T*inv(vcv)) matrix U=mY[p+1:T,]'-mshape(A,n,p*n)*mreg[p+1:T,]' matrix vcv=U*U'/T params A end mle <hansl> >> I found 2 typos in the help pdf for the SVAR package, and the >> references are only "?" (a bibtex problem): >> 1. p10 under 2.4: it's $\frac { n(n-1) }{ 2 } $ restrictions >> 2. p. 21 under SVAR.cumulate: Stores into the model > > Done, thanks. > >>>> a) In his book on page 367 (section 9.1.3) the Rd matrix >>>> (following the notation of Jack) seems to me wrong. > > It is, there's a typo for the R matrix with the constarints for the A > matrix. Element [5,2] of R should be 0 instead of 1. Typical > copy-n-paste mishap. I guess you ought to tell Helmut for the next > edition of his book. > > > -------------------------------------------------- > Riccardo (Jack) Lucchetti > Dipartimento di Economia > > Università Politecnica delle Marche > (formerly known as Università di Ancona) > > r.lucchetti(a)univpm.it > http://www2.econ.univpm.it/servizi/hpp/lucchetti > -------------------------------------------------- > > > _______________________________________________ > Gretl-users mailing list > Gretl-users(a)lists.wfu.edu > http://lists.wfu.edu/mailman/listinfo/gretl-users