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

描述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，我们记录相同现象的多个观测，导致多个不同的时间序列描述相同的变量。将不同的时间序列组合到一个模型中，该模型捕捉相关性并允许预测未来的时间序列值，这是一项艰巨的任务。这个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组合这种时间序列测量，以便能够准确预测未来的值。我们将解决如何最好地结合描述相同现象的多个不同来源的测量结果的问题，此外还将考虑如何使用相依时间序列来帮助我们的预测。这种方法应该能够应对数据缺失、采样不规则、与其他时间序列的未知相关性以及观测数据的不确定性等特点带来的挑战。一个理想的解决方案应该考虑到与每个单独的时间序列相关的不确定性，并旨在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。开发的方法将致力于在计算上高效，并在实质性应用中有效。

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.