Interpretation of DCC-GARCH output

Question

I have done fitted a DCC-GARCH model using the dccfit function from the "rmgarch" package in R. The output is below:

*---------------------------------*
*          DCC GARCH Fit          *
*---------------------------------*

Distribution         :  mvnorm
Model                :  DCC(1,1)
No. Parameters       :  62
[VAR GARCH DCC UncQ] : [0+32+2+28]
No. Series           :  8
No. Obs.             :  240
Log-Likelihood       :  4896.6
Av.Log-Likelihood    :  20.4 

Optimal Parameters
-----------------------------------
                  Estimate   Std. Error  t value  Pr(>|t|)
[FTSE100].mu      0.005599    0.003457 1.6195e+00 0.105339
[FTSE100].omega   0.000100    0.000160 6.2312e-01 0.533205
[FTSE100].alpha1  0.176637    0.124341 1.4206e+00 0.155436
[FTSE100].beta1   0.807578    0.072324 1.1166e+01 0.000000
[MSUSAML].mu      0.007760    0.003077 2.5219e+00 0.011673
[MSUSAML].omega   0.000056    0.000053 1.0484e+00 0.294455
[MSUSAML].alpha1  0.092896    0.040348 2.3023e+00 0.021316
[MSUSAML].beta1   0.886704    0.028933 3.0647e+01 0.000000
[MSEXUK.].mu      0.009228    0.003421 2.6976e+00 0.006984
[MSEXUK.].omega   0.000114    0.000189 6.0293e-01 0.546552
[MSEXUK.].alpha1  0.070957    0.046983 1.5103e+00 0.130978
[MSEXUK.].beta1   0.889084    0.091959 9.6682e+00 0.000000
[DAXINDX].mu      0.010099    0.004489 2.2496e+00 0.024474
[DAXINDX].omega   0.001005    0.000794 1.2650e+00 0.205864
[DAXINDX].alpha1  0.191733    0.113491 1.6894e+00 0.091142
[DAXINDX].beta1   0.600585    0.225184 2.6671e+00 0.007651
[BMUK10Y].mu      0.001496    0.001295 1.1548e+00 0.248181
[BMUK10Y].omega   0.000000    0.000027 0.0000e+00 1.000000
[BMUK10Y].alpha1  0.025774    0.174068 1.4807e-01 0.882287
[BMUK10Y].beta1   0.969964    0.178467 5.4350e+00 0.000000
[BMUS10Y].mu      0.001069    0.001481 7.2147e-01 0.470623
[BMUS10Y].omega   0.000021    0.000014 1.4980e+00 0.134123
[BMUS10Y].alpha1  0.025983    0.024924 1.0425e+00 0.297181
[BMUS10Y].beta1   0.928892    0.037850 2.4542e+01 0.000000
[BMBD10Y].mu      0.000893    0.001088 8.2098e-01 0.411657
[BMBD10Y].omega   0.000000    0.000000 1.2974e-01 0.896774
[BMBD10Y].alpha1  0.000000    0.000089 7.8000e-05 0.999938
[BMBD10Y].beta1   0.999000    0.000075 1.3363e+04 0.000000
[LHUSTRY].mu      0.000170    0.000950 1.7931e-01 0.857694
[LHUSTRY].omega   0.000007    0.000000 2.2820e+01 0.000000
[LHUSTRY].alpha1  0.024463    0.001250 1.9571e+01 0.000000
[LHUSTRY].beta1   0.941022    0.005656 1.6638e+02 0.000000
[Joint]dcca1      0.017443    0.005703 3.0584e+00 0.002225
[Joint]dccb1      0.942324    0.012105 7.7843e+01 0.000000

Information Criteria
---------------------

Akaike       -40.288
Bayes        -39.389
Shibata      -40.388
Hannan-Quinn -39.926

Can someone tell me what is the meaning of Pr(>|t|)? Is it the p value for the parameter? If it is, then I have lots of insignificant parameters which indicates a very bad model I have there. I have tried run examples from the rmgarch.tests folder as well but the Pr(>|t|) values for the example are also big (greater than 0.05). What can I do here?

Those are p-values. Maybe the variables just aren't related to the response. Be aware that you also seem to have 62 parameters, but only 240 data, so you may just not have enough information. — gung - Reinstate Monica, Jan 25 '16 at 16:44
So, does it means it is better for me to have a longer period of observation? @gung — nsaa, Jan 25 '16 at 17:29
I don't know. Someone who knows this material better will have to answer. — gung - Reinstate Monica, Jan 25 '16 at 17:38

score 3 · Accepted Answer · edited Apr 13 '17 at 12:44

3

Yes, the column Pr(>|t|) are the $p$-values.

You should mostly care about the joint significance of (1) alpha1 and beta1 for each of the series and (2) the joint significance of dcca1 and dccb1.

(1) will tell you whether the GARCH(1,1) "makes sense" for the given series. If alpha1 and beta1 are jointly insignificant, you may be better off using constant conditional variance rather than GARCH(1,1).
(2) will tell you whether DCC "makes sense" for the system of series. If dcca1 and dccb1 are jointly insignificant, you may be better off using a constant conditional correlation model rather than DCC(1,1).

You may not care that much about the significance of mu; it is the intercept of the conditional mean model, and there are reasons (not specific to GARCH modelling) for keeping the intercept in even though it is not significant.

Meanwhile, you want to keep omega in the model regardless of its significance unless alpha1+beta1=1, otherwise the absence of omega generates funny patterns in conditional variance -- see this answer for details.

edited Apr 13 '17 at 12:44

Community

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answered Jan 25 '16 at 19:18

Richard Hardy

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From my results,most of the 'alpha1' has value greater than 0.1 which is not significant. So, does it means that I am better to try other model such as Constant Conditional Correlation? – nsaa Jan 25 '16 at 19:59
The reason for this exercise is because I would like to forecast the mean return and variance covariance matrix so that I can use them for portfolio optimization. – nsaa Jan 25 '16 at 20:09
Well, I indicated in my answer that you should look at the joint significance of `alpha1` and `beta1` rather than `alpha1` alone. Besides, `alpha1` is a parameter of the (univariate) GARCH model rather than the DCC part of the DCC-GARCH model. Meanwhile, it is the joint significance of `dcca1` and `dccb1` that indicate whether DCC makes more sense than CCC. – Richard Hardy Jan 25 '16 at 20:32
I will try to run F test to see the joint significance of these parameters. Thanks! – nsaa Jan 26 '16 at 11:47
Is there any reference or articles that I can refer to saying that we need to look at the joint significant of alpha1 and beta1 and we may not care much about the significance of mu and omega? Thanks – nsaa Jan 26 '16 at 14:04
No, I cannot come up with one right away. But the argumentation for the joint significance of `alpha1` and `beta1` as well as `dcca1` and `dccb1` is pretty basic and is not due to research articles but due to core principles of econometric modelling. The argumentation for `mu` is also well established. The only problem is with `omega` where citing a reference could perhaps be useful (but as I said, I do not have a reference ready, unfortunately). – Richard Hardy Jan 26 '16 at 14:08
Okay. I will try to find the information from econometric modelling books. But if you can think any of it, please feel free to let me know here. Thanks! – nsaa Jan 26 '16 at 14:14
You may try Tsay's "Analysis of Financial Time Series" and Zivot's "Modeling Financial Time Series with S-PLUS", but I wouldn't have much hope. – Richard Hardy Jan 26 '16 at 14:20

Interpretation of DCC-GARCH output

1 Answers1