  Several academics have studied the ability of hybrid models mixing univariate
Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models and
neural networks to deliver better volatility predictions than purely
econometric models. Despite presenting very promising results, the
generalization of such models to the multivariate case has yet to be studied.
Moreover, very few papers have examined the ability of neural networks to
predict the covariance matrix of asset returns, and all use a rather small
number of assets, thus not addressing what is known as the curse of
dimensionality. The goal of this paper is to investigate the ability of hybrid
models, mixing GARCH processes and neural networks, to forecast covariance
matrices of asset returns. To do so, we propose a new model, based on
multivariate GARCHs that decompose volatility and correlation predictions. The
volatilities are here forecast using hybrid neural networks while correlations
follow a traditional econometric process. After implementing the models in a
minimum variance portfolio framework, our results are as follows. First, the
addition of GARCH parameters as inputs is beneficial to the model proposed.
Second, the use of one-hot-encoding to help the neural network differentiate
between each stock improves the performance. Third, the new model proposed is
very promising as it not only outperforms the equally weighted portfolio, but
also by a significant margin its econometric counterpart that uses univariate
GARCHs to predict the volatilities.
