Implications of insignificant dccalpha and dccbeta for DCC-model used for co-movement analysis

Question

I'm using a DCC-ARMA(1,0)-GARCH(1,1) model to investigate co-movement of the green bond market and other markets. The ARCH/GARCH parameters of the univariate ARMA(1,0)-GARCH(1,1)models are significant (see table 1) and the Ljung-Box test of their wieghted standardized residuals indicates that the univariate model is sufficent in modelling the respective markets conditional variance (see table 2). Based on this, the univariate model seems fine. However, neither market has both dccalpha and dccbeta as significant with that of the GB market(see table 3). Does this mean that DCC-model I am using is insufficient in modellin the markets co-movement?

Answer 1

There are at least a couple of things that can go wrong:

1. The model's assumptions may be violated, indicating the model is not rich enough to account for patterns in the data.
2. Some of the model's features may be superfluous.

The latter is a lesser evil of the two regarding inference about parameters but a potentially great evil in forecasting. Now in some more detail:

1. Standardized innovations are assumed to be i.i.d. You may assess that e.g. by looking for remaining autocorrelations in levels and/or squares of standardized residuals. They are also assumed to have correlation matrices due to DCC. You may assess that by evaluating whether the covariance matrix of standardized innovations "divided" by the square root of the fitted covariance matrices are diagonal with units on the main diagonal and zeros elsewhere.
   If you see violations of these assumptions, your model can be rejected by the data. Whether a statistically significant finding is also economically significant is another matter, however. E.g. if your sample is very large, even small, economically negligible deviations from the model's assumptions may be detected but they might be relatively innocuous.
2. DCC assumes there is a certain autoregressive structure to the correlation matrix of the standardized innovations. If there is none and the correlation matrices are closer to i.i.d. than to being autoregressive, the structure is superfluous (could be discarded in favor of CCC) and you will find the DCC coefficients to be statistically indistinguishable from zero. The problem is, there seems to be no valid asymptotic (let alone finite-sample) theory for the common DCC model, so there is no way to evaluate the statistical significance. The significance results produced by statistical software should thus be taken with a grain of salt.