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

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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.