Adjustment parameters in VECM - DCC - GARCH model

[Adde]

I estimated a bivariate VECM - DCC - GARCH model by assuming a t-distribution of the residuals. However, none of the error correction terms is statistically significant, although my cointegration tests (Engle-Granger, Johansen) indicate that the chosen time series are cointegrated. When I estimate the same model with a normal distribution and robust standard errors, one of the error correction parameters is statistically significant. I already tried to change the starting values, but unfortunatley of no use. Do you have any further suggestion or explanation why such results are possible?
Kind regards!

[TomDoan]

The first assumption in a GARCH model (univariate or multivariate) is that the residuals are serially uncorrelated. If you're doing a VECM mean model, then your original data are highly serially correlated, so you have to be extremely careful that you have a mean model adequate enough (that is, with enough lags) to make the residuals at least approximately serially uncorrelated. If there is substantial SC left in the residuals, the results from the estimation can be quite poorly behaved.

Be sure that both models have, in fact, converged, and if so, do the standard diagnostic tests for serially correlation and remaining GARCH effects before worrying too much about interpreting the results.

[Adde]

Hi Tom, thanks for the helpful reply! I did all the diagnostics and the model seems robust. However, I realized that one of the time series contains a rather large amount of zeros (appr. 20%), thus no movement. Might this cause the "ugly" behavior of the standard errors or does this only affect the parameter estimations? I am thinking about deleting the zero returns, however, this would distort the empirical results since no return is also an information for the model, right?
Kind regards!

[TomDoan]

Is this a consecutive set of zeros? If so, why would you think that one model would cover that? Also, why would you be using a VECM for return series? They shouldn't even be I(1), much less cointegrated.

[Adde]

I use spot and futures prices. The prices are I(1) and cointegrated. There should thus exist a corresponding VECM model. Yes, some of the zero returns are consecutive.

[TomDoan]

Why are there so many zero returns? Thinly traded?

[Adde]

Yes, in the first years it is a thinly traded market. It becomes way "better" in the later years. My idea is to delete the zero returns as a robustness check, but I do not know whether this is a valid procedure since I randomly change the distances between the observations. I tried weekly returns but then I do not have such strong GARCH effects anymore.
However, RATS converges in most of the cases, irrespective of the fact that it contains zero returns, but I do not know what the zero returns does in the model to the parameters and the standard errors.

[TomDoan]

Why wouldn't you just delete the period when it's thinly traded? It's certainly possible to have sporadic zero returns later, but it sounds as if a single GARCH model across the data range is unlikely to be a correct specification.

Note, BTW, that while the cointegrating rank and estimates of the beta are relatively robust to failures of i.i.d. Normal residuals, the alpha's (adjustment parameters) are estimated using a regression on stationary data, so they are subject to the same type of problems that pretty much any model would have when confronted with fat-tailed residuals (and you have both GARCH and non-Normal conditional residuals).