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:
- Run GARCH on the market returns to get the parameters for volatility over time.
- Create a vector of the volatility over time.
- 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.
- Can I use the three-step procedure to get accurate DCC of the volatility over time?
- 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)?
- 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!