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Is there a package to run simplified multivariate GARCH models in Python? I found the Arch package but that seems to work on only univariate models. I'd like to test out some of the more simple methods described in Bauwends et. al. (2006) like constant conditional correlation.

Python libraries are preferred though I'll play with R as well.

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PYTHON
I have found this class from the statsmodels library for calculating Garch models.
Unfortunately, I have not seen MGARCH class/library. Below you can see the basic information about the garch models in mentioned class from the statsmodels. Probably you have to implement it by your own in python, so this class might be used as a starting point.

roadmap for garch:
* simple case
* starting values: garch11 explicit formulas
* arma-garch, assumed separable, blockdiagonal Hessian
* other standard garch: egarch, pgarch,
* non-normal distributions
* other methods: forecast, news impact curves (impulse response)

R
In R there is a package called mgarch which is available in this github repository and here you can find some examples.

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Slight correction: the package in R is called rmgarch, not mgarch. It works well with rugarch, which provides a variety of univariate GARCH models. Both packages allow for parallelized computation on local cluster and return a nice and full set of fitted parameters, model specs, etc. I provided some additional links in this post.

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