# Get vector of volatility from GARCH-model

Background: Hello, I am trying to investigate the comovement of the logged retuurns of the Green Bond (GB) market and 4 other markets (Treasury Bonds, Corporate Bonds, MSCI World, and Carbon Emission Rights) over time. Previous studies within the field have used DCC-GARCH. I have struggled to understand the methodology of this model. Some sources explain an easy procedure in which you:

1. Run GARCH on the market returns to get the parameters for volatility over time.
2. Create a vector of the volatility over time.
3. Use DCC on the vectors created in step 2.

From other sources it seems as DCC-GARCH is a multivariate GARCH model in which you get the DCC of the volatility over time in one procedure instead of the three intermediate steps as the solution above. The algebra/statistics of this procedure quickly becomes pretty hard and I have not understood it completely.

Questions:

1. Can I use the three-step procedure to get accurate DCC of the volatility over time?
2. I have struggled with the second step in this procedure (using R).
In step 1, I created ARCH/GARCH models to see which best captures the volatility of the markets. Based on the Akaike Information Criterion, GARCH seem to be the better fit. However, how do I use these parameters to get a vector of the volatility over time (i.e. step 2)?
3. As seen in the GARCH model of MSCI World, alpha + beta = 1.002>1 the assumption of unconditional variance being finite and positive is not fulfilled. How do I deal with this?

Would be very greatful for any help!

• Would recommend posting on Quantitative Finance (QF) at StackExchange. Apr 21 at 15:36
• @nxglogic, good idea, though GARCH models (and their extensions) are more actively discussed on Cross Validated (see the count under the GARCH tag here versus there), so the OP's decision to post here first was a smart one. Apr 21 at 17:10

2. You do not have to manually extract results from univariate GARCH models to use them in the DCC model. Check out the rmgarch vignette explaining how the DCC-GARCH model can be implemented in R.
• @Isac, you probably can (I think there is a typo in your last sentence as you are comparing identical models). In rmgarch, you can also use VAR + DCC-GARCH. That is, VAR is the model for the multivariate condtional mean instead of individual AR(1) models. Apr 28 at 19:09