Can I apply the same DCC-GARCH model on sub-samples to investigate differences in co-movements?

Question

I am using DCC-GARCH for a master thesis in which I am investigating the co- movement of the Green bond and other markets pre and during the current economic crisis. Based on the signficant ARCH/GARCH parameters in Table 1 and the failure to reject the null hypothesis of the Ljung-Box test used on the models standardized residuls in Table 2., the ARMA(1,0)-GARCH(1,1) model seems to adequitely fit the conditional variance of the time series.

The graphs below display the DCC(GB,i) (i = Treasury, Carbon, MSCI.World, Carbon) and was computed using DCC-ARMA(1,0)-GARCH(1,1). The dotted line is the divisor of the "pre-crisis" and "during crisis" periods. When looking at them, no difference in the DCC of "pre-crisis" and "during crisis" is shown. I wonder how I should proceed to answer my research quesiton "What are the differences in the co-movements between the GB market and the treasury, corporate, stock, and carbon markets pre and during the Covid-19 crisis period?" Is there any formal test I could do to see if the co-movement has changed, should I just interpret what I see from the graphs or can I run the DCC—ARMA(1,0)-GARCH(1,1) model on two subsets “pre-crisis” and “during crisis” and compare the dccalpha and dccbeta?

Using the same model for the two subperiods intuitively seems wrong since if there is any changes in the markets volatility in-between these two periods, the model created to fit data over the entire period could be a bad fit for at least one of these periods? Or can the model be a good fit for the entire period since it is developed for time series with inconsistent volatility? Another problem of this method would be that I only got 254 observations for the “during crisis period”. Don’t know if this helps in answering the question but since I don’t think it will hurt, I included the graphs of the markets conditional SD. In them we can see that the volatility of the Green Bond, Corporate and stock (MSCI.World’s) markets seem to be a bit higher during crisis than before crisis. To give an idea of the results of this method for comparing the co-movements of the different periods, I included the outputs using the DCC-ARMA(1,0)-GARCH(1,1) model in Table 3 and Table 4.

----------------------------------------DCC GRAPHS--------------------------------------

[

-------------------------------------Conditional SD GRAPHS------------------------------

Answer 1

“What are the differences in the co-movements between the GB market and the treasury, corporate, stock, and carbon markets pre and during the Covid-19 crisis period?“ <...> Using the same model for the two subperiods intuitively seems wrong since if there are any changes in the markets volatility in-between these two periods, the model created to fit data over the entire period could be a bad fit for at least one of these periods? Or can the model be a good fit for the entire period since it is developed for time series with inconsistent volatility?

If the data generating process changes over time, then fitting a single model with time-constant parameters indeed cannot reflect that. It would be a simplification, and an unwelcome one at that if your goal is to assess whether there have been changes and what they have been like. So it would make sense to fit the model on subsamples and compare the results. If you believe some of the model's parameters stay constant over the entire sample period, you could fit the model for the entire period and use some dummies to account for the variations in some parameters (the ones that are not supposed to have stayed constant). A problem with that is that it may not be an option in the software you are using.

Another problem of this method would be that I only got 254 observations for the “during crisis period”

Regarding the sample size and estimation precision, this is a genuine problem. If there is little data, it is fundamentally difficult to estimate a model's parameters, and I am not sure there is any nice way to circumvent this. Simplifying assumptions (such as assuming some parameters stay fixed for the entire sample) may be necessary to make modeling feasible.

(This answer has been moved from another thread, so the quotes might not be 100% accurate, though they were for the original thread.)