Solved – Interpretation of DCC GARCH output In R

garchmultivariate analysisrtime series

I have got clarifications about almost all the aspects of interpretation a DCC model from a post from 2016. But I have a doubt regarding the interpretation of dcca1 and dccb1. The answer there mentions only about the joint (in)significance of the model. But I have obtained some results where dcca1 is insignificant but dccb1 is highly significant.
Does that imply that DCC is inappropriate for my analysis?

One of my results is attached below for reference.

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* DCC GARCH Fit *
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Distribution         :  mvnorm
Model                :  DCC(1,1)
No. Parameters       :  15
[VAR GARCH DCC UncQ] : [0+12+2+1]
No. Series           :  2
No. Obs.             :  201
Log-Likelihood       :  -569.3227
Av.Log-Likelihood    :  -2.83

Optimal Parameters

                   Estimate  Std. Error  t value Pr(>|t|)
[lnm4d1gr].mu      5.963277    0.505299  11.8015 0.000000
[lnm4d1gr].ar1     0.864758    0.041394  20.8909 0.000000
[lnm4d1gr].ma1     0.321100    0.124583   2.5774 0.009955
[lnm4d1gr].omega   0.183493    0.079986   2.2941 0.021787
[lnm4d1gr].alpha1  0.186084    0.077458   2.4024 0.016289
[lnm4d1gr].beta1   0.692538    0.051244  13.5145 0.000000
[lngdpgr].mu       3.006723    0.346063   8.6884 0.000000
[lngdpgr].ar1      0.812573    0.046041  17.6491 0.000000
[lngdpgr].ma1      0.311830    0.075900   4.1084 0.000040
[lngdpgr].omega    0.037324    0.026482   1.4094 0.158721
[lngdpgr].alpha1   0.211533    0.099433   2.1274 0.033388
[lngdpgr].beta1    0.760996    0.085243   8.9273 0.000000
[Joint]dcca1       0.053790    0.040828   1.3175 0.187680
[Joint]dccb1       0.876877    0.057316  15.2990 0.000000

Information Criteria

Akaike       5.8142
Bayes        6.0607
Shibata      5.8040
Hannan-Quinn 5.9139

Best Answer

You can test the appropriateness of the DCC-GARCH (or some other) model by

  1. testing joint significance of its coefficients and
  2. testing whether the model residuals satisfy the assumptions that the model puts on them.

Failing the first test would imply the model is not appropriate. (Failing the second test would imply the same.)

Some other comments:

  1. If the conditional correlation were actually constant, you would expect dcca1 to be approximately zero (insignificantly different from zero) and dccb1 to be approximately 1 (insignificantly different from 1, but significantly different from zero). In your case you have the first but not the second.
    If the true process had dcca1=0 and 0<dccb1<1, that would imply the conditional correlation is declining over time and is asymptoting towards (1-dccb1)/dccb1, similarly to the bottom-right graph in this answer.
  2. An important remark here is that no asymptotic theory for the DCC-GARCH model exists (as of 27 September 2018, AFAIK), except for some step towards it made by McAleer in "Stationarity and invertibility of a dynamic correlation matrix" (2018) and a very recent special case, scalar DCC, by Wang and Pan "A scalar dynamic conditional correlation model: Structure and estimation" (2018). Hence, the estimates of statistical significance are questionable. See also Chang et al. "Volatility Spillovers between Energy and Agricultural Markets: A Critical Appraisal of Theory and Practice" (2018).
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