DCC MGARCH - Beginner's question to multivariate ARCH/GARCH models

[tobias kohler]

Hey there,
i am new to the forum and deeply grateful to have this stata platform.

I have some (more or less) basic questions with analyzing time series. In special i want to predict variances with multivariate GARCH models, which – as things turned out – is not as simple as i first thought. In my studies i always dealt with univariate GARCH type models, so i have a bit trouble understanding the stata output for MGARCH models.

If i would like to estimate a MGARCH DCC model for monthly data (01/2000 – 12/2017) for two indices, i type: 'mgarch dcc (ln_dax ln_estoxx=), arch(1/1) garch(1/1)‘. My output is as follows:

Maybe you could get me some advice with the following (fundamental) questions:

1. Am i right by evaluating both variance processes as reasonable, because each ARCH process does satisfy the non-negativity and stationarity constraint? Do i have to be mindful of something else?

2. How to interprete lambda 1 and 2?

3. What exactly is the interpretation of the correlation coefficient of .96254..? is it a mean of all dynamic correlation coeffiecients?

4. if i perform 'predict var_dcc*, variance' and plot the output, the graph shows 3 types of variances. i have some trouble understanding them. if i for instance need the variance of estoxx for some kind of portfolio optimization problem, do i have to use the variance prediction of "ln_estoxx,ln_estoxx" or of "ln_estoxx,ln_dax"?

sorry for my very basic questions, but i am thankful for all kind of hints and help.

Tobi

[anduong]

- You didn't fit MGARCH, you actually fitted univariate GARCH.
1. Given that you fitted the univariate GARCH, the results look okay. You can use the variance generated from the model.
2. Lamda1 and lamda2 govern the dynamic conditional correlation process. Lamda1 tells us how much the correlation depends on shocks, while lamda2 tells us how much the correlation depends on its own lag.
3. Use ln_estoxx,ln_estoxx because ln_estoxx,ln_dax is the covariance between ln_estoxx and ln_dax