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A New Multilayer Network Construction via Tensor Learning

机译：张量学习的新型多层网络构建

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摘要

Multilayer networks proved to be suitable in extracting and providing dependency information of different complex systems. The construction of these networks is difficult and is mostly done with a static approach, neglecting time delayed interdependences. Tensors are objects that naturally represent multilayer networks and in this paper, we propose a new methodology based on Tucker tensor autoregression in order to build a multilayer network directly from data. This methodology captures within and between connections across layers and makes use of a filtering procedure to extract relevant information and improve visualization. We show the application of this methodology to different stationary fractionally differenced financial data. We argue that our result is useful to understand the dependencies across three different aspects of financial risk, namely market risk, liquidity risk, and volatility risk. Indeed, we show how the resulting visualization is a useful tool for risk managers depicting dependency asymmetries between different risk factors and accounting for delayed cross dependencies. The constructed multilayer network shows a strong interconnection between the volumes and prices layers across all the stocks considered while a lower number of interconnections between the uncertainty measures is identified.
机译：事实证明，多层网络适合于提取和提供不同复杂系统的依赖信息。这些网络的构建很困难，并且大多是通过静态方法完成的，而忽略了时间延迟的相互依存关系。张量是自然代表多层网络的对象，在本文中，我们提出了一种基于Tucker张量自回归的新方法，以便直接从数据构建多层网络。这种方法捕获跨层连接的内部和之间的连接，并利用过滤过程来提取相关信息并改善可视化。我们展示了该方法论在不同固定分数差异财务数据中的应用。我们认为，我们的结果有助于理解金融风险三个不同方面之间的依赖性，即市场风险，流动性风险和波动性风险。实际上，我们展示了所得的可视化结果如何成为风险管理人员的有用工具，用于描述不同风险因素之间的依赖关系不对称并解释延迟的交叉依赖关系。所构建的多层网络显示出所考虑的所有股票的数量和价格层之间的紧密联系，同时确定性不确定性度量之间的联系数量较少。

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