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Dear Tom:
I am a freshman for any GARCH models. I apologize if my question is too simple or stupid.
In simple bi-variate MV-GARCH BEKK(1,1) model, I do not know whether the coefficients of volatility spillover effect (from series 2 to series 1) is A21 or A12. I found both evidence from published papers.
Another qusetion, If a element in metrics B is more than one, Bij>1, are these estimation valid?

Thank you a lot.

hardmann

hardmann wrote:Dear Tom:
I am a freshman for any GARCH models. I apologize if my question is too simple or stupid.
In simple bi-variate MV-GARCH BEKK(1,1) model, I do not know whether the coefficients of volatility spillover effect (from series 2 to series 1) is A21 or A12. I found both evidence from published papers.
Another qusetion, If a element in metrics B is more than one, Bij>1, are these estimation valid?

Thank you a lot.

hardmann

Because the A enters in the form A'u(t-1)u(t-1)'A, A(2,1) gives the weight on the cross effect for lagged residual 2 on variance 1, and A(1,2) would be for 1 on 2.

The off-diagonal B's (and A's) are sensitive to the relative scales and so can be larger than one if they measure the cross effect of a low variance variable on a high variance one.

Dear Tom:

I am still unclear about the interpretation of the BEKK coefficients
for they are quite different from those in typical regressions where
all the coefficients and variables are in common forms, not squared.

Take h11 for example. If we try to express h11 in one single equation, we'll get
h11 = ... + (e1^2*a11^2)+ 2*a11*a21*e2*e1 +(e2^2*a21^2) +
(h11*b11^2)+ 2*b11*h21*b21+(b22*b21^2)
So, h11 will be influenced by squared error e1^2 with a degree of a11^2,
and by the cross influence from asset 2 with 2*a11*a21*e2*e1.
Since all the coefficients and variables are squared or cross-multiply,
does their signs matter??

Could you give us some examples for how to interpret the BEKK coefficients in a economic sense.

Thank in advance.

You're correct that the signs of the matrices aren't determined. Multiply either matrix by -1 and you get the same fit. There is no simple economic interpretation of the individual coefficients on the GARCH term---what matters are particular non-linear functions. The ARCH term is a bit different because the inner matrix is u(t-1)u(t-1)' so the A'u(t-1)u(t-1)'A is the outer product of A'u(t-1), and A'u(t-1) is a vector of linear combinations of the lagged residuals.

Hi Tom

Need to have more clarity on the interpretation of the output from BEKK GARCH estimation.
First a quick estimation of the following:
garch(p=1,q=1,mv=bek,xreg,pmethod=simplex,piters=10,hmatrices=hh,rvectors=rd) / y(1) y(2) y(3) y(4) y(5)
# dum
( the idea was to see the spillover effect of DUM only on conditional variances of the 5 variables)
questions are as follows:
1. why is there no convergence?
2. Which A, B, C is related to h11 (variance of y1) and which one to covariance such as h12, for example?
3. Which Dummy (DUM) is related to variances (h11, h22,...h55) and which one to covariances (h12, ...h45)?

Thank you for your help.

lumengobobo46 wrote:Hi Tom

Need to have more clarity on the interpretation of the output from BEKK GARCH estimation.
First a quick estimation of the following:
garch(p=1,q=1,mv=bek,xreg,pmethod=simplex,piters=10,hmatrices=hh,rvectors=rd) / y(1) y(2) y(3) y(4) y(5)
# dum
( the idea was to see the spillover effect of DUM only on conditional variances of the 5 variables)

Code: Select all

The following outputs were provided:
MV-GARCH, BEKK - Estimation by BFGS
NO CONVERGENCE IN 200 ITERATIONS
LAST CRITERION WAS  0.0326377
Weekly Data From 1996:12:15 To 2012:05:27
Usable Observations                       807
Log Likelihood                    -10866.6004

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  Mean(1)                       0.326588513  0.113787045      2.87017  0.00410247
2.  Mean(2)                       0.315370492  0.079203393      3.98178  0.00006840
3.  Mean(3)                       0.238313252  0.112723004      2.11415  0.03450252
4.  Mean(4)                       0.378775846  0.170293903      2.22425  0.02613177
5.  Mean(5)                       0.042917501  0.108526770      0.39546  0.69250680
6.  C(1,1)                       -0.530884312  0.118287687     -4.48808  0.00000719
7.  C(2,1)                       -0.530408896  0.090766363     -5.84367  0.00000001
8.  C(2,2)                        0.058429483  0.076455093      0.76423  0.44472857
9.  C(3,1)                        0.167181404  0.118715097      1.40826  0.15905489
10. C(3,2)                       -0.237918629  0.182025224     -1.30706  0.19119095
11. C(3,3)                        0.136003983  0.132711805      1.02481  0.30545428
12. C(4,1)                        0.377048050  0.214968631      1.75397  0.07943603
13. C(4,2)                        0.208773337  0.222360254      0.93890  0.34778372
14. C(4,3)                       -0.312319996  0.174457318     -1.79024  0.07341577
15. C(4,4)                       -0.222993583  0.319701087     -0.69751  0.48548588
16. C(5,1)                        0.215626731  0.142678635      1.51128  0.13071826
17. C(5,2)                       -0.426377271  0.261438437     -1.63089  0.10291358
18. C(5,3)                        0.400525460  0.133880484      2.99166  0.00277461
19. C(5,4)                        0.248824126  0.144433606      1.72276  0.08493233
20. C(5,5)                        0.040105658  0.141213303      0.28401  0.77640452
21. A(1,1)                        0.172559568  0.028704842      6.01151  0.00000000
22. A(1,2)                        0.015215170  0.021149903      0.71940  0.47189655
23. A(1,3)                       -0.037199723  0.019479489     -1.90969  0.05617355
24. A(1,4)                       -0.197217304  0.051455731     -3.83276  0.00012672
25. A(1,5)                        0.018551528  0.016994503      1.09162  0.27500045
26. A(2,1)                       -0.002761854  0.046119734     -0.05988  0.95224768
27. A(2,2)                        0.153555362  0.030716028      4.99919  0.00000058
28. A(2,3)                       -0.051466833  0.045082776     -1.14161  0.25361722
29. A(2,4)                       -0.237590076  0.075766255     -3.13583  0.00171369
30. A(2,5)                       -0.104095772  0.029879570     -3.48384  0.00049427
31. A(3,1)                       -0.105253684  0.025761641     -4.08567  0.00004395
32. A(3,2)                       -0.129915294  0.018789928     -6.91409  0.00000000
33. A(3,3)                        0.014841570  0.025544756      0.58100  0.56123870
34. A(3,4)                       -0.029150034  0.046120599     -0.63204  0.52736115
35. A(3,5)                        0.082720875  0.019455240      4.25186  0.00002120
36. A(4,1)                        0.123823498  0.017719267      6.98807  0.00000000
37. A(4,2)                        0.122407094  0.011672222     10.48704  0.00000000
38. A(4,3)                        0.018965029  0.013196593      1.43712  0.15068518
39. A(4,4)                        0.314463396  0.025671395     12.24956  0.00000000
40. A(4,5)                        0.017351847  0.010244069      1.69384  0.09029508
41. A(5,1)                       -0.171419116  0.029899256     -5.73322  0.00000001
42. A(5,2)                       -0.112625877  0.020143186     -5.59126  0.00000002
43. A(5,3)                       -0.052188126  0.029231187     -1.78536  0.07420330
44. A(5,4)                       -0.073195225  0.038789995     -1.88696  0.05916551
45. A(5,5)                        0.117290869  0.020718734      5.66110  0.00000002
46. B(1,1)                        0.992486915  0.010725572     92.53464  0.00000000
47. B(1,2)                        0.008533694  0.010752638      0.79364  0.42740668
48. B(1,3)                        0.028760519  0.012714902      2.26195  0.02370027
49. B(1,4)                        0.154429498  0.023202120      6.65584  0.00000000
50. B(1,5)                       -0.038046599  0.010680009     -3.56241  0.00036746
51. B(2,1)                       -0.073292761  0.027527134     -2.66256  0.00775478
52. B(2,2)                        0.928719678  0.016986791     54.67305  0.00000000
53. B(2,3)                       -0.010694230  0.025405666     -0.42094  0.67379978
54. B(2,4)                        0.351861994  0.034467476     10.20852  0.00000000
55. B(2,5)                       -0.026069118  0.018668016     -1.39646  0.16257635
56. B(3,1)                       -0.024832104  0.018510536     -1.34151  0.17975431
57. B(3,2)                        0.006967922  0.014430807      0.48285  0.62920192
58. B(3,3)                        0.907991813  0.011383360     79.76483  0.00000000
59. B(3,4)                       -0.166556390  0.021906389     -7.60310  0.00000000
60. B(3,5)                       -0.182198047  0.010031647    -18.16233  0.00000000
61. B(4,1)                       -0.086706930  0.010591063     -8.18680  0.00000000
62. B(4,2)                       -0.077781172  0.007582522    -10.25796  0.00000000
63. B(4,3)                        0.005509872  0.008597027      0.64090  0.52158483
64. B(4,4)                        0.850304869  0.013363542     63.62871  0.00000000
65. B(4,5)                        0.018406289  0.007958098      2.31290  0.02072810
66. B(5,1)                        0.190583229  0.015614914     12.20521  0.00000000
67. B(5,2)                        0.135633757  0.012063556     11.24327  0.00000000
68. B(5,3)                        0.258195995  0.014913026     17.31345  0.00000000
69. B(5,4)                        0.147156122  0.025593394      5.74977  0.00000001
70. B(5,5)                        0.988387253  0.009981692     99.02002  0.00000000
71. DUM                           2.438717925  0.360592444      6.76309  0.00000000
72. DUM                           1.460514925  0.326697817      4.47054  0.00000780
73. DUM                           1.014803359  0.214303683      4.73535  0.00000219
74. DUM                           0.473890618  0.330720545      1.43290  0.15188542
75. DUM                           0.688477363  0.358453387      1.92069  0.05477097
76. DUM                          -0.141587715  0.464153606     -0.30504  0.76033191
77. DUM                           0.264413172  0.710749129      0.37202  0.70987766
78. DUM                          -1.478444731  0.730489445     -2.02391  0.04297944
79. DUM                           0.294994838  0.838024662      0.35201  0.72482917
80. DUM                           0.222388589  0.695837612      0.31960  0.74927279
81. DUM                          -0.280411755  0.322230295     -0.87022  0.38417933
82. DUM                           0.545345803  0.372227846      1.46509  0.14289746
83. DUM                          -0.399408023  0.400938139     -0.99618  0.31916092
84. DUM                          -0.248758291  0.412743039     -0.60270  0.54671141
85. DUM                          -0.040361355  0.420567990     -0.09597  0.92354545

questions are as follows:
1. why is there no convergence?

The default limit is 200 main iterations. You obviously need more than that. Increase to ITERS=1000 or so.

lumengobobo46 wrote: 2. Which A, B, C is related to h11 (variance of y1) and which one to covariance such as h12, for example?

I think that's discussed in the thread above.

lumengobobo46 wrote: 3. Which Dummy (DUM) is related to variances (h11, h22,...h55) and which one to covariances (h12, ...h45)?

They are in the same order as the C. It's a lower triangular matrix. Other than the first element (which is the shift in h11), the other shifts aren't simple functions of the coefficients.