This paper presents a novel dynamic network autoregressive conditional heteroscedasticity (ARCH) model based on spatiotemporal ARCH models to forecast volatility in the US stock market. To improve the forecasting accuracy, the model integrates temporally lagged volatility information and information from adjacent nodes, which may instantaneously spill across the entire network. The model is also suitable for high-dimensional cases where multivariate ARCH models are typically no longer applicable. We adopt the theoretical foundations from spatiotemporal statistics and transfer the dynamic ARCH model for processes to networks. This new approach is compared with independent univariate log-ARCH models. We could quantify the improvements due to the instantaneous network ARCH effects, which are studied for the first time in this paper. The edges are determined based on various distance and correlation measures between the time series. The performances of the alternative networks' definitions are compared in terms of out-of-sample accuracy. Furthermore, we consider ensemble forecasts based on different network definitions.

翻译：本文提出一种基于时空自回归条件异方差（ARCH）模型的新型动态网络自回归条件异方差模型，用于预测美国股票市场波动率。为提高预测精度，该模型整合了时序滞后波动率信息及相邻节点的信息，此类信息可能瞬时扩散至整个网络。该模型同样适用于多元ARCH模型通常不再适用的高维情形。我们采纳时空统计的理论基础，将针对过程的动态ARCH模型迁移至网络环境。这种新方法与独立单变量对数自回归条件异方差模型进行了比较。我们能够量化瞬时网络ARCH效应带来的改进，本文首次对此类效应进行研究。边基于时间序列间的多种距离与相关性度量确定。我们比较了不同网络定义在样本外预测精度方面的表现。此外，还考虑了基于不同网络定义的集成预测。