The RATS Software Forum

Dear Tom Doan,
Thank you for you reply to my earlier posts. I have another issue that I need some clarification. I am estimating a simple VECH model in RATS and the model achieves convergence when I do not include asymmetry. However, when I include the asymmetric model, it becomes difficult to achieve convergence. I want to ask if there is a way of achieving convergence in the simple VECH model even if asymmetry is added to the model. I have provided the output results of the model below. Secondly, I want to ask if it is valid to estimate the mean equation of the VECH model separately using a Vector Autoregression (VAR). Finally, I am not sure what the Cs in the output results are. I know what the As and Bs measure, and I thought the Cs are the constants but am not sure.
Thank you always for your kind replies.

GARCH(P=1,Q=1,PMETHOD=SIMPLEX,PITERS=10) / DLGSECI DLEXR DLSP500 DLCOP

MV-GARCH - Estimation by BFGS
Convergence in 105 Iterations. Final criterion was 0.0000071 <= 0.0000100
Monthly Data From 1991:02 To 2015:12
Usable Observations 299
Log Likelihood 2132.1644

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(1) 0.008943745 0.002608487 3.42871 0.00060646
2. Mean(2) 0.000444626 0.000246683 1.80242 0.07147942
3. Mean(3) 0.009085187 0.002076891 4.37442 0.00001218
4. Mean(4) 0.009327796 0.005046392 1.84841 0.06454320
5. C(1,1) 0.000590777 0.000115113 5.13214 0.00000029
6. C(2,1) 0.000012430 0.000018922 0.65691 0.51123722
7. C(2,2) 0.000000885 0.000000647 1.36818 0.17125636
8. C(3,1) 0.000004241 0.000117360 0.03614 0.97117387
9. C(3,2) -0.000033680 0.000021687 -1.55299 0.12042466
10. C(3,3) 0.000066167 0.000032946 2.00833 0.04460819
11. C(4,1) -0.000079545 0.000180530 -0.44062 0.65948812
12. C(4,2) -0.000011580 0.000040603 -0.28521 0.77548675
13. C(4,3) -0.000047511 0.000165347 -0.28734 0.77385278
14. C(4,4) 0.006574589 0.001086507 6.05113 0.00000000
15. A(1,1) 1.094146283 0.200973425 5.44423 0.00000005
16. A(2,1) 0.687649763 0.151205848 4.54777 0.00000542
17. A(2,2) 1.324321585 0.166194484 7.96851 0.00000000
18. A(3,1) 0.154744776 0.072671475 2.12937 0.03322330
19. A(3,2) 0.049020394 0.019895238 2.46393 0.01374245
20. A(3,3) 0.176575809 0.052225311 3.38104 0.00072212
21. A(4,1) 0.186573319 0.107540059 1.73492 0.08275511
22. A(4,2) -0.009847946 0.032652655 -0.30160 0.76295923
23. A(4,3) 0.164710477 0.069015059 2.38659 0.01700556
24. A(4,4) 0.289490432 0.075641539 3.82714 0.00012964
25. B(1,1) 0.193851185 0.056162203 3.45163 0.00055721
26. B(2,1) -0.126937640 0.142559403 -0.89042 0.37324080
27. B(2,2) 0.468609250 0.029970081 15.63590 0.00000000
28. B(3,1) -0.360866256 0.298546503 -1.20874 0.22676126
29. B(3,2) -0.926170866 0.036879141 -25.11368 0.00000000
30. B(3,3) 0.799139913 0.048480962 16.48358 0.00000000
31. B(4,1) -0.148412300 0.366234764 -0.40524 0.68530246
32. B(4,2) -0.891225134 0.171591790 -5.19387 0.00000021
33. B(4,3) 0.009317683 0.327188603 0.02848 0.97728090
34. B(4,4) -0.215136391 0.101412444 -2.12140 0.03388813

The C's are the variance constants.

You clearly have a major problem, I suspect because you're using log series rather than returns, so you have highly serially correlated residuals and are doing nothing about that.

Can you estimate a VAR first, and do the GARCH on the residuals? Yes. However, standard practice is to do a joint estimate. How you do that is covered in the User's Guide.

Hi Tom,
Many thanks for the reply to my post. Your suggestions are well noted. The output results I provided is just an example of what I am doing. It is actually not the final result. However, my concern is that the model does not converge when I include asymmetry. As well as dealing with the autocorrelation, I thought something can be done to achieve convergence even if I include asymmetry in the model. Do you think there is anything I can do to achieve convergence in the asymmetric simple VECH model?
Thank you

The fact that you can't get a GARCH model to converge when you are failing badly at assumption #1 of the GARCH model (serially uncorrelated residuals) isn't that surprising. Get that fixed and see what happens.