Beginner problems in DCC-GARCH

[ashu+123]

results cc garch with varma has convergence.pdf

the 2nd last results of CC GARCH is showing convergence.

(143.14 KiB) Downloaded 1630 times

You can read more about VARIANCES=VARMA at

https://estima.com/ratshelp/index.html? ... tput_VARMA

It does tend to be hard to use as the number of variables increases. Until you have a model which converges you shouldn't worry too much about the tests for residual ARCH. Make sure you have an adequate mean model (checking for serial correlation in the mean) before worrying too much about that.

hey Tom,
thanks for your quick reply.
when I'm running DCC and CC without VARMA variance they are converging. but with VARMA variance they are not.
I was making changes in the code and I came across that in one of the code CC is converging with VARMA variance. But now I'm not able to found which code its.
I am attaching the code and output please let me know whether results are correct.

Please let me know whether I'm doing the correct thing or not.

[TomDoan]

If there some type of timing issue with your series? Your RIBOV seems to be running a period ahead of the other four series. (It has large and very significant lag coefficients in the other four mean models).

You estimated some models without the VAR model (just means) and those seem to converge better, but that's not really helpful because you definitely need the lag (because of the effect described above).

[ashu+123]

Thanks, tom for your quick reply

can you suggest what can be done to solve such a problem? Since the BEKK model is converging with the VAR model.
And CC is converging without VAR(mean model). Is it necessary to converge CC and DCC with a mean model?

In the code given in garchmv.rpf in CC and DCC model, there is not mean model specified. And can you explain the reason behind adding the mean model in CC and DCC?

And is the diagnostic testing of the BEKK model is correct or not

[TomDoan]

This is your data set. I've pointed out that there seems to be a timing issue with the RIBOV series. GARCH models assume that the different data series are aligned---it appears that your RIBOV is close to being dated a period ahead of the others.

The data in GARCHMV.RPF are a set of exchange rates taken from prices in a single market, so they naturally align and the optimal lags using SBC is 0 (fairly clearly). It's possible that your series are individually fairly close to being random walks with GARCH errors (which means that a CC model which fits individual random walks with GARCH errors might seem to work well), but with serial correlation between the series (due to timing problems).

[ashu+123]

hey, tom
thanx for your quick response

these are diagnostic of VAR(1)-BEKK GARCH.
Can you tell me they are correct or not? Can you help me with the interpretation?

Code: Select all

MV-GARCH, BEKK - Estimation by BFGS
Convergence in   259 Iterations. Final criterion was  0.0000058 <=  0.0000100

With Heteroscedasticity/Misspecification Adjusted Standard Errors
Usable Observations                      3736
Log Likelihood                    -30233.6036

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
Mean Model(RIBOV)
1.  RIBOV{1}                     -0.050834813  0.016017048     -3.17379  0.00150460
2.  RMOEX{1}                      0.030222066  0.016285875      1.85572  0.06349310
3.  RSENSEX{1}                    0.020751177  0.019258169      1.07753  0.28124537
4.  RSHCOMP{1}                    0.020709638  0.014682271      1.41052  0.15838617
5.  RJALSH{1}                     0.013177361  0.028638991      0.46012  0.64543039
6.  Constant                      0.053220273  0.026911946      1.97757  0.04797717
Mean Model(RMOEX)
7.  RIBOV{1}                      0.150314578  0.012843823     11.70326  0.00000000
8.  RMOEX{1}                     -0.054912239  0.018480708     -2.97133  0.00296515
9.  RSENSEX{1}                    0.012801772  0.021756852      0.58840  0.55626258
10. RSHCOMP{1}                   -0.017608760  0.012616562     -1.39569  0.16280907
11. RJALSH{1}                     0.001768272  0.022823056      0.07748  0.93824375
12. Constant                      0.090143500  0.021926715      4.11113  0.00003937
Mean Model(RSENSEX)
13. RIBOV{1}                      0.117804355  0.010022617     11.75385  0.00000000
14. RMOEX{1}                      0.005083363  0.013808715      0.36813  0.71277840
15. RSENSEX{1}                   -0.001293662  0.016273145     -0.07950  0.93663752
16. RSHCOMP{1}                   -0.023368915  0.010504528     -2.22465  0.02610463
17. RJALSH{1}                     0.055429341  0.015774677      3.51382  0.00044172
18. Constant                      0.074425814  0.018158440      4.09869  0.00004155
Mean Model(RSHCOMP)
19. RIBOV{1}                      0.087911026  0.009545879      9.20932  0.00000000
20. RMOEX{1}                      0.032804272  0.015760106      2.08148  0.03739041
21. RSENSEX{1}                   -0.000186599  0.017357370     -0.01075  0.99142259
22. RSHCOMP{1}                   -0.022804828  0.012426434     -1.83519  0.06647802
23. RJALSH{1}                     0.042495680  0.020117279      2.11240  0.03465241
24. Constant                      0.011847663  0.026622461      0.44503  0.65630164
Mean Model(RJALSH)
25. RIBOV{1}                      0.145613477  0.010083825     14.44030  0.00000000
26. RMOEX{1}                     -0.017061558  0.010887361     -1.56710  0.11709186
27. RSENSEX{1}                    0.004468033  0.014733991      0.30325  0.76170192
28. RSHCOMP{1}                   -0.013192569  0.010616670     -1.24263  0.21400502
29. RJALSH{1}                    -0.057455731  0.016108702     -3.56675  0.00036143
30. Constant                      0.072253711  0.015936270      4.53392  0.00000579

31. C(1,1)                        0.121973929  0.122904225      0.99243  0.32098746
32. C(2,1)                        0.080976116  0.164290476      0.49288  0.62209469
33. C(2,2)                        0.239141731  0.060264894      3.96818  0.00007242
34. C(3,1)                       -0.062814799  0.212267548     -0.29592  0.76728907
35. C(3,2)                        0.036352026  0.069600952      0.52229  0.60146698
36. C(3,3)                       -0.101849220  0.134592998     -0.75672  0.44921760
37. C(4,1)                       -0.032209625  0.030554241     -1.05418  0.29180119
38. C(4,2)                        0.020615916  0.034795655      0.59249  0.55352562
39. C(4,3)                        0.026920039  0.073299556      0.36726  0.71342464
40. C(4,4)                        0.019646786  0.080208611      0.24495  0.80649817
41. C(5,1)                       -0.061946712  0.208755532     -0.29674  0.76666284
42. C(5,2)                        0.091516333  0.062957817      1.45361  0.14605349
43. C(5,3)                       -0.044250716  0.257885933     -0.17159  0.86375966
44. C(5,4)                        0.080893660  0.086533692      0.93482  0.34987968
45. C(5,5)                        0.000000785  0.136988233  5.73141e-06  0.99999543
46. A(1,1)                        0.103792091  0.036311128      2.85841  0.00425770
47. A(1,2)                       -0.020804085  0.029558686     -0.70382  0.48154298
48. A(1,3)                       -0.023401598  0.021958670     -1.06571  0.28655425
49. A(1,4)                       -0.028519390  0.013622363     -2.09357  0.03629817
50. A(1,5)                       -0.019158922  0.021195325     -0.90392  0.36603672
51. A(2,1)                       -0.006521309  0.026161455     -0.24927  0.80315066
52. A(2,2)                        0.353546027  0.042851193      8.25055  0.00000000
53. A(2,3)                        0.006469321  0.030407722      0.21275  0.83151997
54. A(2,4)                       -0.020534524  0.012064523     -1.70206  0.08874440
55. A(2,5)                        0.052073426  0.013904813      3.74499  0.00018040
56. A(3,1)                        0.038512158  0.037682145      1.02203  0.30676827
57. A(3,2)                       -0.048614130  0.038874574     -1.25054  0.21110311
58. A(3,3)                        0.209114418  0.041500660      5.03882  0.00000047
59. A(3,4)                       -0.030595144  0.028578444     -1.07057  0.28436408
60. A(3,5)                       -0.004652494  0.029615220     -0.15710  0.87516756
61. A(4,1)                        0.015316210  0.083271754      0.18393  0.85406803
62. A(4,2)                       -0.013012894  0.051529838     -0.25253  0.80063047
63. A(4,3)                       -0.009720888  0.038058206     -0.25542  0.79839749
64. A(4,4)                        0.174260255  0.014389114     12.11056  0.00000000
65. A(4,5)                       -0.016869054  0.035427784     -0.47615  0.63396522
66. A(5,1)                        0.102012844  0.066865773      1.52564  0.12710049
67. A(5,2)                       -0.026555901  0.061581967     -0.43123  0.66630222
68. A(5,3)                        0.076224854  0.028389413      2.68497  0.00725353
69. A(5,4)                        0.072150274  0.025795020      2.79706  0.00515696
70. A(5,5)                        0.199448779  0.030738539      6.48856  0.00000000
71. B(1,1)                        0.993412345  0.012290264     80.82921  0.00000000
72. B(1,2)                        0.005173289  0.017345291      0.29825  0.76550990
73. B(1,3)                        0.015252192  0.016948721      0.89990  0.36817228
74. B(1,4)                        0.005796467  0.005541165      1.04607  0.29552701
75. B(1,5)                        0.022715072  0.012984462      1.74940  0.08022118
76. B(2,1)                        0.016602661  0.008422473      1.97123  0.04869716
77. B(2,2)                        0.931757367  0.017075619     54.56653  0.00000000
78. B(2,3)                       -0.001892073  0.013932553     -0.13580  0.89197755
79. B(2,4)                        0.010088799  0.004874199      2.06984  0.03846758
80. B(2,5)                       -0.014803737  0.006168449     -2.39991  0.01639899
81. B(3,1)                       -0.014013321  0.014845813     -0.94392  0.34520844
82. B(3,2)                        0.018481813  0.012589701      1.46801  0.14210136
83. B(3,3)                        0.972389264  0.012837871     75.74381  0.00000000
84. B(3,4)                        0.003021175  0.008675819      0.34823  0.72766797
85. B(3,5)                        0.000795545  0.008113568      0.09805  0.92189167
86. B(4,1)                       -0.002801299  0.019561926     -0.14320  0.88613096
87. B(4,2)                       -0.000379815  0.011334006     -0.03351  0.97326702
88. B(4,3)                        0.002380258  0.010099011      0.23569  0.81367153
89. B(4,4)                        0.983229650  0.002588865    379.79171  0.00000000
90. B(4,5)                        0.000973309  0.008952816      0.10872  0.91342825
91. B(5,1)                       -0.049095746  0.016998643     -2.88822  0.00387434
92. B(5,2)                       -0.002236706  0.025088599     -0.08915  0.92896090
93. B(5,3)                       -0.028938983  0.013756850     -2.10361  0.03541289
94. B(5,4)                       -0.016010662  0.010444184     -1.53297  0.12528229
95. B(5,5)                        0.961452188  0.007906960    121.59568  0.00000000


Information Criteria
AIC          16.236
SBC          16.394
Hannan-Quinn 16.292
(log) FPE    16.236


Independence Tests for Series Z1
Test            Statistic  P-Value
Ljung-Box Q(20)  27.099089     0.1325
McLeod-Li(20)    83.302551     0.0000
Turning Points   -1.099666     0.2715
Difference Sign  -1.615005     0.1063
Rank Test        -1.175040     0.2400


Independence Tests for Series Z2
Test            Statistic  P-Value
Ljung-Box Q(20)  4.2773703     0.9999
McLeod-Li(20)    5.1763381     0.9996
Turning Points  -1.1772897     0.2391
Difference Sign -1.2183373     0.2231
Rank Test       -2.4679522     0.0136


Independence Tests for Series Z3
Test            Statistic  P-Value
Ljung-Box Q(20)  35.382134     0.0182
McLeod-Li(20)    28.448706     0.0992
Turning Points   -2.225207     0.0261
Difference Sign  -3.315011     0.0009
Rank Test        -2.106193     0.0352


Independence Tests for Series Z4
Test            Statistic  P-Value
Ljung-Box Q(20)  35.747788     0.0165
McLeod-Li(20)    47.256721     0.0005
Turning Points   -1.216101     0.2239
Difference Sign  -3.938346     0.0001
Rank Test         0.000368     0.9997


Independence Tests for Series Z5
Test            Statistic  P-Value
Ljung-Box Q(20)   41.21270     0.0035
McLeod-Li(20)    321.78551     0.0000
Turning Points    -2.14758     0.0317
Difference Sign   -3.20168     0.0014
Rank Test         -1.91096     0.0560


Multivariate Q Test
Test Run Over 3 to 3738
Lags Tested         10
Degrees of Freedom 250
Q Statistic        312.2989
Signif Level         0.0045


Multivariate ARCH Test
Statistic Degrees Signif
  2132.20    1125 0.00000


Multivariate Q Test
Test Run Over 3 to 3738
Lags Tested          40
Degrees of Freedom 1000
Q Statistic        1085.309
Signif Level          0.031


Multivariate ARCH Test
Statistic Degrees Signif
 12617.45    9000 0.00000

As you mentioned in the earlier threads that I have run my CC and DCC without a mean model and they are converging. And not converging with the mean model what does that mean. Is it mean my data doesn't fit with CC and DCC models.

[TomDoan]

I just explained that. You really need to look into the source and timing of your data.

Regarding the BEKK results, the McLeod-Li tests on the first and (particularly) the fifth series aren't good.

[ashu+123]

thanks, tom for your reply,
sorry if the question is wrong.
Mcleod li test is not good for 2 series. what should be done to correct them.

[TomDoan]

You have a typo on this (the (3) should be (5))

set z5 = rd(t)(3)/sqrt(hh(t)(5,5))

which will probably take care of the problem with series 5.

You can't take five arbitrary returns series, slap them into a multivariate GARCH model and expect them to work.

[curiousresearcher]

Hello, I am facing non convergence issues for the following data for daily returns. The commands used are as follows. I also tried adding nlpar(derives=second) before garch instruction, but it did not help. Please advice what to. The commands used and results as as follows (data attached)

garch(p=1,q=1,mv=dcc) / RCMCG RBRENT

MV-DCC GARCH - Estimation by BFGS
NO CONVERGENCE IN 40 ITERATIONS. FINAL NORMED GRADIENT 0.00008
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY DIFFERENT SETTING FOR EXACTLINE, DERIVES OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES/PMETHOD OPTION MIGHT ALSO WORK

Usable Observations 993
Log Likelihood NA

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(RFMCG) 0.097688004 0.028604493 3.41513 0.00063752
2. Mean(RBRENT) 0.073017195 0.044426689 1.64354 0.10027053

3. C(1) 0.024807476 0.010303436 2.40769 0.01605382
4. C(2) 0.056644522 0.020004282 2.83162 0.00463129
5. A(1) 0.054567260 0.013709691 3.98020 0.00006886
6. A(2) 0.057287323 0.013706971 4.17943 0.00002922
7. B(1) 0.924921792 0.019090336 48.44974 0.00000000
8. B(2) 0.927611685 0.015849975 58.52449 0.00000000
9. DCC(A) -0.015081393 0.017446845 -0.86442 0.38735748
10. DCC(B) -0.050000000 0.020371471 -2.45441 0.01411149

garch(p=1,q=1,mv=dcc) / RTELECOM RBRENT

MV-DCC GARCH - Estimation by BFGS
NO CONVERGENCE IN 87 ITERATIONS. FINAL NORMED GRADIENT 7.84075e+10
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY DIFFERENT SETTING FOR EXACTLINE, DERIVES OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES/PMETHOD OPTION MIGHT ALSO WORK

Usable Observations 993
Log Likelihood NA

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(RTELECOM) 0.168206298 0.006343585 26.51597 0.00000000
2. Mean(RBRENT) 0.285022081 0.025259863 11.28360 0.00000000

3. C(1) 2.473059551 0.355483175 6.95690 0.00000000
4. C(2) 0.184114995 0.003552487 51.82707 0.00000000
5. A(1) 0.399174222 0.055092869 7.24548 0.00000000
6. A(2) 0.138620350 0.006751855 20.53071 0.00000000
7. B(1) -0.032810644 0.140059411 -0.23426 0.81478133
8. B(2) 0.817193639 0.005968131 136.92621 0.00000000
9. DCC(A) -0.014806258 0.000022017 -672.50689 0.00000000
10. DCC(B) -0.049840959 0.000119313 -417.73119 0.00000000

garch(p=1,q=1,mv=dcc) / RBANKEX RBRENT
MV-DCC GARCH - Estimation by BFGS
NO CONVERGENCE IN 44 ITERATIONS. FINAL NORMED GRADIENT 0.00068
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY DIFFERENT SETTING FOR EXACTLINE, DERIVES OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES/PMETHOD OPTION MIGHT ALSO WORK

Usable Observations 993
Log Likelihood NA

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(RBANKEX) 0.123491937 0.039406646 3.13378 0.00172568
2. Mean(RBRENT) 0.083599242 0.041806769 1.99966 0.04553720

3. C(1) 0.036029881 0.015715755 2.29260 0.02187126
4. C(2) 0.057653228 0.020121834 2.86521 0.00416736
5. A(1) 0.073111437 0.014014194 5.21696 0.00000018
6. A(2) 0.054873114 0.009867248 5.56114 0.00000003
7. B(1) 0.916517323 0.013978036 65.56839 0.00000000
8. B(2) 0.928744085 0.012216305 76.02496 0.00000000
9. DCC(A) -0.012013326 0.000068552 -175.24509 0.00000000
10. DCC(B) -0.050000000 0.044083491 -1.13421 0.25670587

garch(p=1,q=1,mv=dcc) / ROILGAS RBRENT
MV-DCC GARCH - Estimation by BFGS
NO CONVERGENCE IN 18 ITERATIONS. FINAL NORMED GRADIENT 1.18281e+09
ESTIMATION POSSIBLY HAS STALLED OR MACHINE ROUNDOFF IS MAKING FURTHER PROGRESS DIFFICULT
TRY DIFFERENT SETTING FOR EXACTLINE, DERIVES OR ALPHA ON NLPAR
RESTARTING ESTIMATION FROM LAST ESTIMATES OR DIFFERENT INITIAL GUESSES/PMETHOD OPTION MIGHT ALSO WORK

Usable Observations 993
Log Likelihood NA

Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. Mean(ROILGAS) -0.044657816 0.013933222 -3.20513 0.00135001
2. Mean(RBRENT) 0.150178216 0.004115484 36.49102 0.00000000

3. C(1) 0.734122369 0.032797851 22.38325 0.00000000
4. C(2) 0.687720922 0.037301324 18.43690 0.00000000
5. A(1) 0.325029851 0.011841350 27.44872 0.00000000
6. A(2) 0.331039272 0.011091352 29.84661 0.00000000
7. B(1) 0.435382301 0.005320221 81.83538 0.00000000
8. B(2) 0.572192043 0.013693253 41.78642 0.00000000
9. DCC(A) -0.006523890 0.000081996 -79.56318 0.00000000
10. DCC(B) -0.050000567 0.002274839 -21.97983 0.00000000


.

[TomDoan]

DCC works best when the series

1. have fairly high contemporaneous correlation and
2. have relatively similar dynamics

I'm not sure what are your other series are, but RBRENT I assume is the return on Brent oil price. It's not clear that that will satisfy either of those when paired with stock returns. Note that if CC is adequate, the parameters of DCC aren't identified (a=b=0 and a=0,b=1 should both give the same log likelihood). In your case, it looks like CC is a better option with all three of those.

[curiousresearcher]

DCC works best when the series

1. have fairly high contemporaneous correlation and
2. have relatively similar dynamics

I'm not sure what are your other series are, but RBRENT I assume is the return on Brent oil price. It's not clear that that will satisfy either of those when paired with stock returns. Note that if CC is adequate, the parameters of DCC aren't identified (a=b=0 and a=0,b=1 should both give the same log likelihood). In your case, it looks like CC is a better option with all three of those.

Hi- in the research paper i am referring to studies oil and stock market return across three countries. Here the correlation between oil and stock market returns is 0.07, 0.025 and 0.14 which is not very high and still they have used DCC.

The research paper in questions is available at https://www.researchgate.net/publicatio ... _countries

Kindly help if possible, though i understand this can take time

[TomDoan]

Unfortunately, that's a really bad paper. (I mean really). It looks like it was largely copied and pasted from other papers and then they slapped in results that weren't even checked very carefully. Note: they run four different GARCH models, most of which fail some important diagnostics without any mention of that (i.e. they ran models for someone else's data), and, on top of that, never provide the log likelihoods of the models.

[curiousresearcher]

Unfortunately, that's a really bad paper. (I mean really). It looks like it was largely copied and pasted from other papers and then they slapped in results that weren't even checked very carefully. Note: they run four different GARCH models, most of which fail some important diagnostics without any mention of that (i.e. they ran models for someone else's data), and, on top of that, never provide the log likelihoods of the models.

Thanks a ton. I will look to refer to some A* star journals only from now on. Quite shocked as this journal was in B category in ABDC list and i couldn't even think that papers can get published without proper review .

I am really honored and grateful to have be a part of this forum. The guidance i am getting is priceless especially for a newcomer to research like me.

[curiousresearcher]

Dear Tom,

I am facing a problem with the attached dataset where in BEKK GARCH, i can see A(1,2), a(2,1), B(1,2), B(2,1) cross spillover coeffecients in Bekk garch, but the coeffecients are missing in case of both DCC and CC garch. Kindly advise the change in code needed . This is a two asset financial asset returns series data

The codes used are
DATA(FORMAT=XLSX,ORG=COLUMNS,LEFT=2) 1 1111 RETURNSA returnsb
GARCH(P=1,Q=1,MV=BEKK,robusterrors,stdresids=rstd,DIST=GED) / RETURNSA returnsb
GARCH(P=1,Q=1,MV=dcc,robusterrors,stdresids=rstd,DIST=GED) / RETURNSA returnsb
GARCH(P=1,Q=1,MV=cc,robusterrors,stdresids=rstd,DIST=GED) / RETURNSA returnsb

[TomDoan]

DCC and CC are heavily restricted models which don't provide for any "spillover" effects in the variances.

Have you read the article in the newsletter about spillover tests?

https://estima.com/newslett/Apr2019RATSLetter.pdf