The RATS Software Forum

Posted: **Sun Mar 13, 2016 5:49 pm**

Hello,
I am estimating volatility in four variables using a multivariate GARCH-BEKK Model. I am not very sure how the results of the GARCH-BEKK model from RATS are interpreted. I have pasted the results below.
For example, I am not sure what the alphabets C, A, B, and D in the results stand for. I assume that they are the matrices where C is constant, A is the ARCH, B is the GARCH, and D is the asymmetric effects. Please I want to know if this is correct. Also, for matrix C, all the pairs of the elements are not reported. I would like someone to explain to me why the pairs for matrix C are very limited.

Code: Select all

   GARCH(P=1,Q=1,MV=BEKK,ASYMMETRIC) / DLEXR DLGSMKT DLCOP DLUSSMKT

MV-GARCH, BEKK - Estimation by BFGS
Convergence in   174 Iterations. Final criterion was  0.0000044 <=  0.0000100
Monthly Data From 1991:01 To 2012:12
Usable Observations                       264
Log Likelihood                      1774.9006

    Variable                            Coeff           Std Error          T-Stat       Signif
*************************************************************************************
1.  Mean(1)                       0.001947115  0.000438964       4.43571  0.00000918
2.  Mean(2)                       0.010425618  0.003158901       3.30039  0.00096549
3.  Mean(3)                       0.005192512  0.005472075       0.94891  0.34266589
4.  Mean(4)                       0.007173422  0.002050331       3.49867  0.00046759
5.  C(1,1)                        0.001738218  0.000645786       2.69163  0.00711037
6.  C(2,1)                        0.018816366  0.008763924       2.14703  0.03179128
7.  C(2,2)                        0.018488934  0.006026322       3.06803  0.00215475
8.  C(3,1)                        0.046161431  0.015431154       2.99144  0.00277662
9.  C(3,2)                       -0.046591052  0.015744329      -2.95923  0.00308411
10. C(3,3)                       -0.000000359  0.031179674 -1.14981e-005  0.99999083
11. C(4,1)                       -0.006251824  0.003392724      -1.84272  0.06537059
12. C(4,2)                       -0.004805567  0.004623720      -1.03933  0.29865169
13. C(4,3)                       -0.000000001  0.005100631 -2.65172e-007  0.99999979
14. C(4,4)                       -0.000000067  0.003996564 -1.68518e-005  0.99998655
15. A(1,1)                        0.629822852  0.054738909      11.50594  0.00000000
16. A(1,2)                       -2.236442666  0.472514472      -4.73307  0.00000221
17. A(1,3)                        0.074443566  0.303901186       0.24496  0.80648758
18. A(1,4)                        0.351468252  0.134403754       2.61502  0.00892227
19. A(2,1)                       -0.072957923  0.011421775      -6.38762  0.00000000
20. A(2,2)                       -1.166496179  0.134832825      -8.65143  0.00000000
21. A(2,3)                       -0.075796780  0.090603867      -0.83657  0.40283243
22. A(2,4)                        0.050701138  0.031658283       1.60151  0.10926344
23. A(3,1)                       -0.018757425  0.007991165      -2.34727  0.01891153
24. A(3,2)                       -0.427011089  0.084240614      -5.06895  0.00000040
25. A(3,3)                        0.058429344  0.080206364       0.72849  0.46631514
26. A(3,4)                       -0.000544349  0.029422443      -0.01850  0.98523906
27. A(4,1)                       -0.121927562  0.016204998      -7.52407  0.00000000
28. A(4,2)                       -1.517812801  0.130520823     -11.62889  0.00000000
29. A(4,3)                        0.198921428  0.138095996       1.44046  0.14973797
30. A(4,4)                       -0.167793165  0.056616819      -2.96366  0.00304001
31. B(1,1)                        0.840913920  0.020003312      42.03873  0.00000000
32. B(1,2)                        0.375086453  0.172609432       2.17304  0.02977763
33. B(1,3)                       -0.278390831  0.145269111      -1.91638  0.05531673
34. B(1,4)                       -0.033463815  0.052876532      -0.63287  0.52682046
35. B(2,1)                       -0.056260760  0.006756335      -8.32711  0.00000000
36. B(2,2)                       -0.055510349  0.052183747      -1.06375  0.28744294
37. B(2,3)                       -0.145457222  0.052250271      -2.78386  0.00537169
38. B(2,4)                        0.112662982  0.022153370       5.08559  0.00000037
39. B(3,1)                       -0.019027401  0.009987156      -1.90519  0.05675576
40. B(3,2)                        0.071123998  0.099883079       0.71207  0.47641986
41. B(3,3)                        0.292527325  0.111884462       2.61455  0.00893455
42. B(3,4)                       -0.118215337  0.039873355      -2.96477  0.00302909
43. B(4,1)                       -0.006341631  0.012497788      -0.50742  0.61185998
44. B(4,2)                        0.409431534  0.121031328       3.38286  0.00071736
45. B(4,3)                        0.226156666  0.150304646       1.50466  0.13241275
46. B(4,4)                        0.759481459  0.039681841      19.13927  0.00000000
47. D(1,1)                       -0.332312691  0.313581089      -1.05973  0.28926541
48. D(1,2)                       -4.027081859  2.299698096      -1.75114  0.07992266
49. D(1,3)                        1.570183456  2.159797950       0.72700  0.46722302
50. D(1,4)                       -0.904476144  0.865371499      -1.04519  0.29593596
51. D(2,1)                       -0.033410640  0.013918122      -2.40051  0.01637209
52. D(2,2)                       -0.802153030  0.168277384      -4.76685  0.00000187
53. D(2,3)                        0.283432025  0.120819361       2.34592  0.01898040
54. D(2,4)                        0.035192820  0.040889111       0.86069  0.38940919
55. D(3,1)                       -0.001289339  0.010387810      -0.12412  0.90121996
56. D(3,2)                       -0.120833384  0.071673016      -1.68590  0.09181547
57. D(3,3)                        0.401215462  0.116076571       3.45647  0.00054730
58. D(3,4)                       -0.018447779  0.057442711      -0.32115  0.74809603
59. D(4,1)                        0.019342979  0.030970243       0.62457  0.53225555
60. D(4,2)                        0.021655476  0.244965332       0.08840  0.92955701
61. D(4,3)                        0.232094249  0.215904019       1.07499  0.28238006
62. D(4,4)                        0.550155794  0.090079613       6.10744  0.00000000

Thank you so much
Kind regards

Muta

Posted: **Sun Mar 13, 2016 6:29 pm**

See

https://estima.com/ratshelp/garchmvrpf. ... utput_BEKK

The variance "constant" is symmetric, so it can't have more free elements than this. It's parametrized by its lower triangle. BTW, your second and third variables seem to have relatively weak "GARCH" effects.

Posted: **Thu May 12, 2016 11:46 pm**

Hi Tom,
I am using six time series variables, i.e., futures returns of six agricultural crops. I am interested in finding the volatility spill over from one variable to other. I am using the following code for estimation of VAR-bekk model:
*
system(model=var1)
variables dlbarfpsq dlwheatfpsq dlcorifpsq dlgramfpsq dlzeerafpsq dlmustfpsq
lags 1 2
det constant
end(system)
*
garch(model=var1,p=1,q=1,mv=bekk,method=bfgs,iters=500,$
pmethod=simplex,piters=10,robusterrors,rvectors=rbekk,hmatrices=hbekk,stdresids=zu)

However, there is a convergence problem. Could you please suggest me the code so that there is a convergence.
Regards,
Sanjeev

Posted: **Fri May 13, 2016 7:15 am**

How much data do you have? That's a big model.

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