Approaching Modern Problems in Multivariate Time Series via Network Modelling and State-Space Methods.

描述某一特定变量如何随时间演变的时间索引观测序列称为时间序列。在许多应用中，我们记录同一现象的多次观测，导致描述同一变量的多个不同时间序列。将不同的时间序列组合到一个模型中，以捕获依赖关系并允许预测未来的时间序列值，这是一项艰巨的任务。该项目是与一个行业合作伙伴合作的，旨在开发一种有效的方法来结合这些时间序列测量，以便准确预测未来的价值。除了考虑如何使用相关时间序列来帮助我们进行预测外，我们还将讨论如何最好地结合来自多个不同来源的测量结果来描述同一现象。这种方法应该能够处理诸如数据缺失、不规则采样、与其他时间序列的未知依赖关系以及观测结果的不确定性等特征所带来的挑战。理想的解决方案将考虑到与每个单独的时间序列相关的不确定性，并将致力于最小化和量化组合预测的不确定性。此外，它将能够确定单个时间序列的最佳可能组合，并在发生某些变化的情况下调整该组合。所开发的方法旨在提高计算效率，并在实际应用中有效。

A sequence of time indexed observations, describing how a particular variable evolves with time, is referred to as a time series. In many applications, we record multiple observations of the same phenomena, leading to multiple different time series describing the same variable. The challenge of combining the differing time series into one model, which captures the dependencies and allows the prediction of future time series values, is a non-trivial task. This project is in collaboration with an industry partner, and aims to develop an effective method for the combination of such time series measurements in order to enable accurate predictions of future values.We will be addressing the question of how best to combine measurements from multiple different sources describing the same phenomenon, in addition to considering how dependent time series can be used to aid our predictions. This method should be able to deal with challenges presented by characteristics such as missing data, irregular sampling, unknown dependencies with other time series and uncertainty about the observations. An ideal solution will take into account the uncertainties associated with each individual time series, and will aim to minimise and quantify the uncertainty of the combined prediction. Furthermore, it will be able to determine the best possible combination of the individual time series, and adapt this combination in the case that some change occurs. The developed method will aim to be computationally efficient, and effective in substantive applications.