Dynamic covariance modeling with artificial neural networks

Abstract

This article proposes a novel multivariate generalized autoregressive conditionally heteroscedastic (GARCH) model that incorporates the modified Cholesky decomposition for a covariance matrix in order to reduce the number of covariance parameters and increase the interpretation power of the model. The modified Cholesky decomposition for covariance matrix reduces the number of covariance parameters to $p(p+1)/2$, where p is the dimension of the stocks in the data, and enables us to obtain a regression equation. To account for the nonlinearity in the GARCH model, the parameters in our model are modeled using long short-term memory. The proposed model is compared with DCC model with respect to portfolio optimization and the distances between the actual covariance matrices and predicted covariance matrices. It is found that although the distances may or may not be reduced by our proposed model in different cases presented in this article, our proposed model outperforms the DCC model in terms of mean portfolio returns.

KEYWORDS:

• Conditional heteroscedasticity
• dynamic conditional correlation
• GARCH
• long short-term memory
• volatility modeling