Time Series Forecasting with Graphical Structure

多变量时间序列预测模型在整个科学领域无处不在，特别是在工程和金融领域。最常用的模型认为数据是任意的，并依赖于学习的参数来建模相互依赖性。然而，在许多现实世界的场景中，底层系统具有额外的固有结构，可以用图形表示并利用这些结构来产生更准确和可解释的预测。这方面的例子包括流行病学中的疾病传播、交通流量建模和金融中的协方差建模。传统的预测方法通常难以有效地处理这些类型的问题，因为相对于可用数据可能涉及非常大量的参数（如经典的自回归模型），或者部署起来非常昂贵（如许多深度学习解决方案）。然而，通过利用数据的底层结构，通常可以同时避免过拟合并降低所涉及的计算复杂性。开发和部署利用这一点的预测方案是一个新兴的和有前途的研究方向。 经验相似性模型将预测建立为与测试输入最密切相关的先前观察到的数据点的直接函数。为此，它们由两个基本组成部分组成--相似性模型和组合相似观测结果以构建预测的方法。他们有几个有吸引力的属性，使他们在实践中很有用：-他们不需要任何培训和新的数据可以集成在持续的基础上，没有额外的成本-他们是高度模块化的：组件可以自由互换，即使在预测时间-他们是快速和高度可解释的实践经验相似性方法已部署在金融环境中，特别是在波动率预测的巨大影响。我们打算适应和发展这些方法，以更好地适应网络结构化数据，特别是协方差预测的相关问题。金融资产的协方差矩阵在现代资产管理中发挥着核心作用-准确的预测对于管理投资组合风险和定价选项至关重要。尽管如此，关于这一主题的研究相对较少，简单的向量异质自回归（VHAR）模型仍然与更复杂和计算昂贵的最先进的模型竞争。我们已经看到，通过利用这个问题的网络结构，可以获得比使用基于经验相似性的管道的VHAR模型更好的上级结果，同时保持高度的可解释性。在这个领域还有很多工作要做：- 正确的相似性概念是管道成功的核心，这涉及到网络嵌入技术的高度活跃领域-类似地，构造函数的选择可以对准确性产生重大影响，一个考虑很少在文献中探讨到目前为止-非-数据的稳定性意味着最佳结果往往不是通过单一模型，而是通过适合不同制度的各种模型组合获得的;- 创建非常适合时间序列数据的动态集成方案是另一个有前途的研究课题。我们打算继续扩大这些观测，可解释的预测，适合在实践中部署。由于其高度灵活的模块化结构，我们希望由此产生的管道族不仅适用于协方差预测问题，而且更广泛地适用于任何具有图形结构的预测应用程序。该项目属于以下EPSRC研究领域：人工智能技术，统计和应用概率福尔斯。

Multivariate time series forecasting models are ubiquitous throughout the sciences, particularly in engineering and finance contexts. The most commonly used models consider the data as arbitrary and depend on the learned parameters to model interdependencies. In many real-world scenarios however, the underlying system has additional inherent structure which can be represented graphically and exploited to yield more accurate and interpretable predictions. Examples of this include disease propagation in epidemiology, traffic flow modelling and covariance modelling in finance. Traditional forecasting methods often struggle to effectively handle these types of problems due to the potentially very large number of parameters involved relative to the available data (as in classical autoregressive models) or are extremely computationally expensive to deploy (as in many deep learning solutions). By utilising the underlying structure of the data however, it is often possible to simultaneously avoid overfitting and reduce the computational complexity involved. Developing and deploying forecasting schemes which take advantage of this is a fledging and promising direction of research. Empirical similarity models build forecasts as a direct function of the previously observed data points most closely related to the test input. To do so, they consist of two fundamental components- a model of similarity and a means of combining similar observations to construct a forecast. They have several attractive properties which make them useful in practice: -they do not require any training and new data can be integrated on an ongoing basis at no additional cost -they are highly modular: the components can be freely interchanged even at forecast time -they are fast and highly interpretable in practice Empirical similarity methods have been deployed to great effect in financial contexts, particularly in volatility forecasting. We intend to adapt and develop these methods to better suit network structured data, in particular to the related problem of covariance forecasting. Covariance matrices of financial assets play a central role in modern asset management- accurate forecasting is critical for example to managing portfolio risk and pricing options. Despite this, the body of research on this topic is relatively modest, with simple vector heterogeneous autoregressive (VHAR) models still performing competitively with much more complex and computationally expensive state of the art models. We have seen that by exploiting the network structure of this problem, it is possible to attain superior results to VHAR models using an empirical similarity-based pipeline, while retaining a high degree of interpretability. There remains much to be done in this space: -the correct notion of similarity is central to the success of the pipeline, and this touches on the highly active field of network embedding techniques -similarly, the choice of construction function can have a significant impact on accuracy, a consideration scarcely explored in the literature to date -the non-stationary nature of the data means that the best results are often attained not through a single model but through diverse ensembles of models suited to different regimes; -the creation of dynamic ensembling schemes well-suited to time series data is another promising topic of research We intend to continue to expand on these observations with the aim of producing fast, interpretable forecasts suitable for deployment in practice. Due to its highly flexible modular structure, we hope that the resulting family of pipelines will be applicable not only to covariance forecasting problems but more broadly to any forecasting application with graphical structure. This project falls within the following EPSRC research areas: artificial intelligence technologies, statistics and applied probability.