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 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 shortterm memory, show improved forecast accuracy respect to existing econometric models.

中文翻译：

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用于预测多元已实现波动率的 Cholesky-ANN 模型

准确预测多元波动率对金融业起着至关重要的作用。此处介绍的 Cholesky-Artificial Neural Networks 规范为此主题提供了双重优势。一方面，Cholesky 分解的使用确保了肯定的预测。另一方面，人工神经网络的实现允许在没有任何特定分布假设的情况下指定非线性关系。样本外比较表明人工神经网络无法明显优于竞争模型。然而，长记忆检测网络，如具有外生输入和长短期记忆的非线性自回归模型过程，显示出相对于现有计量经济学模型的预测准确性有所提高。