Restricted MV-GARCH

Discussions of ARCH, GARCH, and related models

Re: Restricted MV-GARCH

function MyU time
type vector MyU
type integer time
*
dim MyU(n)
ewise MyU(i)=r(i)(time)-e(i)(time)
end
frml Lt = hh=EGARCHSpillover(t),%pt(hhs,t,hh),y=MyU(t),rd=%xt(u,t),%logdensity(hh,rd)
TomDoan

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

Re: Restricted MV-GARCH

Dear Tom,

I hope that you are very well. Sorry for this trivial question and I am highly grateful to you for all your help throughout my work. In the code you posted above for the estimation of CC-VARMA-GARCH model using maximize (thank you very much for providing the code)[reference: MacAleer et al 2009], I am concerned and would like to make sure with the interpretation of the parameters:

13. VCV(1) 0.13407299 1.23262965 0.10877 0.91338501
14. VCV(2) 0.03921416 5.31144995 0.00738 0.99410931
15. VCV(3) 0.28495410 22.17374276 0.01285 0.98974669
16. VB(1,1) 0.01761675 0.43374925 0.04062 0.96760279
17. VB(2,1) 0.01889646 0.67426563 0.02803 0.97764201
18. VB(3,1) 0.00678185 0.74354425 0.00912 0.99272261
19. VB(1,2) -0.01383489 0.10465773 -0.13219 0.89483262
20. VB(2,2) 0.01055315 0.05128463 0.20578 0.83696586
21. VB(3,2) -0.01743545 0.47217117 -0.03693 0.97054391
22. VB(1,3) 0.03605749 0.23669159 0.15234 0.87891913
23. VB(2,3) -0.01368431 0.08404284 -0.16283 0.87065592
24. VB(3,3) 0.15556198 0.72299108 0.21516 0.82963910
25. VA(1,1) 1.02254387 0.64081011 1.59570 0.11055468
26. VA(2,1) -0.05692978 1.94433074 -0.02928 0.97664137
27. VA(3,1) 0.26217073 4.04532499 0.06481 0.94832661
28. VA(1,2) 0.09937098 0.40245156 0.24691 0.80497467
29. VA(2,2) 0.95971767 0.31714389 3.02613 0.00247708
30. VA(3,2) 0.32594252 1.80943362 0.18014 0.85704650
31. VA(1,3) -0.16417414 0.38467536 -0.42679 0.66953506
32. VA(2,3) 0.05829499 0.05058386 1.15244 0.24913930
33. VA(3,3) 0.33500067 0.20060691 1.66994 0.09493206
34. QC(1,1) 0.29592910 0.07175644 4.12408 0.00003722
35. QC(2,1) 0.11536369 0.27213818 0.42392 0.67162719
36. QC(2,2) 0.06919854 0.04205292 1.64551 0.09986446

VB(2,1) is shocks in 2 to affect variance of 1 and VB(1,2) would be shocks in 1 to affect variance of 2.
VA(2,1) is volatility spillover from 2 to 1 and VA(1,2) is from 1 to 2.
and so on.

Am I right about this interpretation (direction of causality)? I just would like to make sure whether I am correct or not.

I made great progress over using RATS and there is still to be done, though. I really appreciate your valuable help and motivating me to develop myself using RATS.

Many thanks for your great help and feedback
Faek
FaeK

Posts: 36
Joined: Tue Jan 03, 2012 9:01 pm

Re: Restricted MV-GARCH

Dear all,

Because of the way the VARMA-GARCH model (ref: McAleer et al 2009) is set up, A(1,2) [or VB(1,2) as above] would be shocks in 2 to affect variances of 1 and A(2,1) would be shocks in 1 to affect variances of 2, is not it?

I really appreciate any comments or hints to make sure of this?

Many thanks
Faek
FaeK

Posts: 36
Joined: Tue Jan 03, 2012 9:01 pm

Re: Restricted MV-GARCH

It looks like the labeling on the output is backwards from what is described in the manual. Yes, as you read that, VB(i,j) is shock i to variable j.
TomDoan

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

Re: Restricted MV-GARCH

Dear Tom,

Thank you so much for all your help and patience. As the labeling on the output is backwards, I thought that VB(i,j) is shock j to variable i. I attached the theoretical model to this post. If the coefficients are entering the matrices as in the attached file (in line with Tsay example 10.5), so VB(1,2) is shocks of 2 on variable 1. By replicating Tsay data using the above code, I realized that this is indeed the way Tsay interpreted his results in example 10.5.

If I am wrong, could you guide me where exactly this has been discussed in the manual because I could not find it.

Many thanks for all your great help. Indeed I try to acknowledge you and RATS team whenever I present my work.
Faek
FaeK

Posts: 36
Joined: Tue Jan 03, 2012 9:01 pm

Previous