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st: Volatility IRF


From   "Michael Ralph M. Abrigo" <mmabrigo@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Volatility IRF
Date   Thu, 27 Dec 2012 23:14:55 -1000

Happy holidays, listers!

Has anyone estimated volatility IRFs (Hafner, C.M. and H. Herwatz
(2006). Volatility impulse responses for multivariate GARCH models: An
exchange rate illustration. Journal of International Money and
Finance, 25) before? I am trying to replicate the one that Hafner and
Herwatz have in the paper using GARCH(1,1)-BEKK, and I can't get the
numbers/routine right. Any help would be much appreciated. Below is
what I have done (and failed) so far:

* start ---------------------------------------------------------------
// Input data matrices from Hafner and Herwatz (2006), p. 732
* A1 matrix
     mat A  = 0.271, -0.055 \ -0.047, 0.290
* B1 matrix
     mat B  = 0.954,  0.016 \  0.012, 0.950
* Residual
     mat e0 = 0.0221, 0.0321
* Conditional variance
     mat s0 = 0.000011960, 0.000009620 \ 0.000009620, 0.000009940
* Compute IRF for t=1
     matrix symei V D = s0
     mat s0_ = V*cholesky(diag(D))*V'  // conditional variance square root
     mat e0std = s0_*inv(s0)*e0'           // standardized residual
     mat v1 = A*(s0_*e0std*e0std'*s0_-s0)
* end ------------------------------------------------------------------


Many thanks. And happy holidays.

Sincerely,
Michael
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