## STRUCTRESIDS-Structural Innovations (revised)

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### STRUCTRESIDS-Structural Innovations (revised)

This procedure converts the standard VAR residuals into the equivalent structural innovations.

Revised 27 March 2011 to add WEIGHTS and SIGMA options.

The syntax is:

@StructResids(options) u start end v

Parameters:
u = VECT[SERIES] of VAR residuals (input)
start end = range to convert
v = VECT[SERIES] of structural innovations (output)

The transformation from u's to v's can be specified in one of two ways: either a matrix F is provided using the FACTOR option that makes u=Fv or a matrix W is provided using the WEIGHTS option that makes Wu=v. If F isn't a full NxN matrix, then the covariance matrix of u is also needed to do compute the weight matrix which solves for v (the formula for the weight matrix is tr(F)*inv(SIGMA)). By default, that will be the standard %SIGMA matrix; if it's some other matrix, you can input it using the SIGMA option. The three forms are thus:

@StructResids(FACTOR=F) u start end v
@StructResids(WEIGHTS=W) u start end v
@StructResids(FACTOR=F,SIGMA=S) u start end v

where the first is used if F is a full N x N factor of the covariance matrix, the second is used if you have a P x N matrix of weights to construct the structural residuals from the VAR residuals, and the last is used if F is an N x P part of a factorization.

structresids.src
TomDoan

Posts: 2725
Joined: Wed Nov 01, 2006 5:36 pm

### Re: StructResids-Procedure to create structural innovations

Hi, this seems to be very useful.
For a simple Choleski would it correct to use the %sigma matrix as factor?
@StructResids(factor=%sigma)
Thanks
Alberto
Alberto

Posts: 17
Joined: Tue May 06, 2008 8:14 am

### Re: StructResids-Procedure to create structural innovations

Alberto wrote:Hi, this seems to be very useful.
For a simple Choleski would it correct to use the %sigma matrix as factor?
@StructResids(factor=%sigma)
Thanks
Alberto

No. It would be @StructResids(factor=%decomp(sigma))

Last bumped by TomDoan on Sun Mar 27, 2011 5:28 am.
TomDoan

Posts: 2725
Joined: Wed Nov 01, 2006 5:36 pm