This paper presents a dynamic network autoregressive conditional heteroscedasticity (ARCH) model suitable for high-dimensional cases where multivariate ARCH models are typically no longer applicable.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 processes to networks. The model integrates temporally lagged volatility and information from adjacent nodes, which may instantaneously spill across the entire network. The model is used to forecast volatility in the US stock market, and the edges are determined based on various distance and correlation measures between the time series. The performance of alternative network definitions is compared with independent univariate log-ARCH models in terms of out-of-sample prediction accuracy. The results indicate that more accurate forecasts are obtained with network-based models and that accuracy can be improved by combining the forecasts of different network definitions. We emphasise the significance for practitioners to integrate network structure information when developing volatility forecasts.

本文提出了一种动态网络自回归条件异方差 (ARCH) 模型，适用于多元 ARCH 模型通常不再适用的高维情况。我们采用时空统计的理论基础，并将动态 ARCH 模型过程转移到网络中。该模型集成了暂时滞后的波动性和来自相邻节点的信息，这些信息可能会立即溢出到整个网络。该模型用于预测美国股市的波动性，其边缘是根据时间序列之间的各种距离和相关性度量来确定的。在样本外预测精度方面，将替代网络定义的性能与独立单变量 log-ARCH 模型进行了比较。结果表明，基于网络的模型可以获得更准确的预测，并且可以通过结合不同网络定义的预测来提高准确性。我们强调从业者在制定波动性预测时整合网络结构信息的重要性。