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mgao6767 committed Oct 1, 2023
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Expand Up @@ -8,7 +8,7 @@ Introduction
The Multivariate GARCH(1,1) model generalizes the univariate :doc:`/algorithms/garch`
framework to multiple time series, capturing not only the conditional variances
but also the conditional covariances between the series. One common form is the
**Constant Conditional Correlation (CCC) model** proposed by Robert Engle (1991).
**Constant Conditional Correlation (CCC) model** proposed by Bollerslev (1990).

.. tip:: Check `Examples`_ section for code guide and comparison to Stata.

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In the bivariate case, the log-likelihood function can be specifically written as a function of all parameters.

The log-likelihood function :math:`\ell` for the bivariate case with all parameters :math:`\Theta = (\omega_1, \alpha_1, \beta_1, \omega_2, \alpha_2, \beta_2, \rho)` is:
The log-likelihood function :math:`\ell` for the bivariate case with all parameters :math:`\Theta = (\mu_1, \omega_1, \alpha_1, \beta_1, \mu_2, \omega_2, \alpha_2, \beta_2, \rho)` is:

.. math::
:label: log_likelihood_bivariate
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