Solved – Interpretation of DCC-GARCH output

garchmultivariate analysisrtime seriesvolatility-forecasting

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?

Best Answer

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.

Related Question