Cholesky–ANN models for predicting multivariate realized volatility

Accurately forecasting multivariate volatility plays a crucial role for the financial industry. The Cholesky–artificial neural networks specification here presented provides a twofold advantage for this topic. On the one hand, the use of the Cholesky decomposition ensures positive definite forecasts. On the other hand, the implementation of artificial neural networks allows us to specify nonlinear relations without any particular distributional assumption. Out‐of‐sample comparisons reveal that artificial neural networks are not able to strongly outperform the competing models. However, long‐memory detecting networks, like nonlinear autoregressive model process with exogenous input and long short‐term memory, show improved forecast accuracy with respect to existing econometric models.