MGARCH with robust option

[veryconfusedmgarch]

Hi,

I'm just wondering what is the "Shape" variable in the output list? Thank you!

35. B(3,2) -0.005499489 0.035456768 -0.15510 0.87673928
36. B(3,3) 0.896992221 0.056335815 15.92224 0.00000000
37. D(1,1) -0.413873540 0.201963278 -2.04925 0.04043753
38. D(1,2) -0.056871036 0.148981136 -0.38173 0.70265932
39. D(1,3) -0.082628288 0.196626169 -0.42023 0.67431717
40. D(2,1) 0.139429640 0.111785271 1.24730 0.21228794
41. D(2,2) 0.125871036 0.119963035 1.04925 0.29406376
42. D(2,3) 0.260242432 0.174949814 1.48753 0.13687589
43. D(3,1) -0.033990898 0.232293675 -0.14633 0.88366304
44. D(3,2) 0.032736530 0.079845480 0.41000 0.68180702
45. D(3,3) 0.022555454 0.219113052 0.10294 0.91801075
46. Shape 4.315635446 0.417152618 10.34546 0.00000000

Best,
veryconfusedmgarch

[TomDoan]

I assume you must have done DISTRIB=T. That's the estimate for the degrees of freedom.

[veryconfusedmgarch]

I assume you must have done DISTRIB=T. That's the estimate for the degrees of freedom.

Thanks Tom! I can't help but to think that you know everything. Just another minor issues,

The code

Code: Select all

compute gstart=764,gend=912
garch(p=1,q=1,DIST=T,ROBUST,model=varmodel,mv=bekk,pmethod=simplex,piters=10,iters=600,rseries=rs3,mvhseries=hhs3,$
stdresids=zu3,derives=dd3) gstart gend xhk xSH xSZ

@mvqstat(lags=40) 764 912
# zu3
@mvarchtest(lags=1) 764 912
# zu3
@flux 764 912
# dd3

The output

Code: Select all

MV-GARCH, BEKK - Estimation by BFGS
Convergence in   149 Iterations. Final criterion was  0.0000090 <=  0.0000100

With Heteroscedasticity/Misspecification Adjusted Standard Errors
Daily(5) Data From 2014:02:25 To 2014:11:13
Usable Observations                       188
Log Likelihood                      -555.3424

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
Mean Model(XHK)
1.  XHK{1}                       -0.078151545  0.069172523     -1.12981  0.25855790
2.  XSH{1}                        0.140270179  0.109396747      1.28222  0.19976714
3.  XSZ{1}                       -0.126049989  0.069778945     -1.80642  0.07085297
4.  Constant                      0.053484576  0.039704055      1.34708  0.17795416
Mean Model(XSH)
5.  XHK{1}                       -0.087498112  0.072450148     -1.20770  0.22716231
6.  XSH{1}                        0.153317727  0.113270743      1.35355  0.17587967
7.  XSZ{1}                       -0.096933089  0.079330896     -1.22188  0.22175180
8.  Constant                      0.074341945  0.045020659      1.65129  0.09868037
Mean Model(XSZ)
9.  XHK{1}                       -0.105927325  0.099042414     -1.06951  0.28483777
10. XSH{1}                        0.111295395  0.178052984      0.62507  0.53192579
11. XSZ{1}                       -0.036053566  0.125564861     -0.28713  0.77401201
12. Constant                      0.163017517  0.064678456      2.52043  0.01172116

13. C(1,1)                        0.382470532  0.098745454      3.87330  0.00010737
14. C(2,1)                        0.593115983  0.092312563      6.42508  0.00000000
15. C(2,2)                        0.213586442  0.192878420      1.10736  0.26813698
16. C(3,1)                        0.875029535  0.177760311      4.92252  0.00000085
17. C(3,2)                        0.393717519  0.332922651      1.18261  0.23696391
18. C(3,3)                        0.000050192  0.133425320  3.76178e-04  0.99969985
19. A(1,1)                       [b]-0.131871383[/b]  0.125841915     -1.04791  0.29467867
20. A(1,2)                        0.192327965  0.141619121      1.35806  0.17444308
21. A(1,3)                        0.338396647  0.169460526      1.99691  0.04583545
22. A(2,1)                        0.093420244  0.195224538      0.47853  0.63227505
23. A(2,2)                      [b] -0.053250530[/b]  0.189948323     -0.28034  0.77921498
24. A(2,3)                       -0.867526609  0.273529137     -3.17161  0.00151599
25. A(3,1)                       -0.109726826  0.131575875     -0.83394  0.40431290
26. A(3,2)                        0.065066425  0.175502989      0.37074  0.71082930
27. A(3,3)                        0.697943173  0.239111921      2.91890  0.00351272
28. B(1,1)                        0.914924934  0.061146155     14.96292  0.00000000
29. B(1,2)                       -0.055080891  0.017491290     -3.14905  0.00163804
30. B(1,3)                       -0.143422211  0.066220231     -2.16584  0.03032366
31. B(2,1)                       -0.067102610  0.059563475     -1.12657  0.25992300
32. B(2,2)                        0.956635464  0.026865024     35.60896  0.00000000
33. B(2,3)                        0.181215144  0.058373693      3.10440  0.00190667
34. B(3,1)                       -0.157322791  0.187511972     -0.83900  0.40146857
35. B(3,2)                       -0.370814026  0.160514013     -2.31017  0.02087896
36. B(3,3)                        0.171566240  0.338873860      0.50628  0.61265765
37. Shape                         5.899240616  1.382654778      4.26660  0.00001985



Multivariate Q(40)=     332.51533
Significance Level as Chi-Squared(360)=       0.84769



Test for Multivariate ARCH
Statistic Degrees Signif
    49.09      36 0.07161



Test  Statistic  P-Value
Joint 5.71626391    0.67

    1 0.06657886    0.76
    2 0.04813217    0.88
    3 0.07941952    0.68
    4 0.07713696    0.69
    5 0.07172764    0.73
    6 0.38622554    0.08
    7 0.13028353    0.44
    8 0.05250911    0.85
    9 0.12613994    0.45
   10 0.45541286    0.05
   11 0.16931731    0.32
   12 0.08933429    0.62
   13 0.02133529    1.00
   14 0.09743487    0.58
   15 0.14768400    0.38
   16 0.16731941    0.33
   17 0.10968478    0.52
   18 0.06970912    0.74
   19 0.18000256    0.30
   20 0.20064091    0.26
   21 0.16879401    0.32
   22 0.07943319    0.68
   23 0.08420800    0.65
   24 0.18024973    0.30
   25 0.09430062    0.60
   26 0.05962863    0.81
   27 0.11934626    0.48
   28 0.19314619    0.27
   29 0.07447320    0.71
   30 0.08086528    0.67
   31 0.06841900    0.75
   32 0.03688863    0.95
   33 0.04303499    0.91
   34 0.15432858    0.36
   35 0.03500505    0.96
   36 0.02345649    0.99
   37 0.08286846    0.66

I am concerned about the diagonal of A and B matrices do not have the same sign. According to the user manual, A and -A are the same but I suppose it is conditional on the diagonal having the same sign. Since uniqueness requires A(1,1), B(1,1) to be positive in the bivariate case, then it requires A(1,1), A(2,2) and B(1,1) and B(2,2) to have the same sign. Therefore, from the results above, I don't have uniqueness as they don't have the same sign. If I am correct, does it mean that the model is still fine as I don't have a GARCH/ARCH parameter exceeds one? I supposed that I have done the estimation correctly (i.e. the model is converging, white noise, stability of parameters and no arch effect with 1 lag, DoF estimate is significant.

Thank you very much in advance!

[TomDoan]

Why are you using so little of your data? 188 data points isn't much for a model that complicated. Whatever is your 3rd series seems to have very "unGARCH" properties at least during this part of the sample.

[veryconfusedmgarch]

Hi Tom,

The total sample size is about 900. But this will be separated into three sub-samples and hence the reduced sub-sample you saw just. Do you think it is a huge problem with this sample size?

Would you consider the model is valid given that it has a negative A(1,1) and A(2,2), and a positive A(3,3)?

Thanks tom!

[TomDoan]

First of all, the stability condition for a BEKK model depends upon the A and B matrices in their entirety---it can be unstable with all coefficient below 1 and can be stable with some above it. What concerns me when I look at those results is the B(3,3). The other B diagonal elements are typical of a GARCH model.