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Title: A model for dynamic processes on networks Authors:  Matthew Nunes - Lancaster University (United Kingdom) [presenting]
Kathryn Leeming - University of Bristol (United Kingdom)
Marina Knight - University of York (United Kingdom)
Guy Nason - Imperial College, London (United Kingdom)
Abstract: Analysis problems are considered for time series that are observed at nodes of a potentially large network structure. Such problems commonly appear in a vast array of fields, such as environmental data or epidemiology, or measurements from computer system monitoring. The time series observed on the network might exhibit different characteristics such as nonstationary behaviour or strong correlation, and the nodal series evolve according to the inherent spatial structure. We will introduce the network autoregressive / moving average processes: a set of flexible models for network time series. For fixed networks the models are essentially equivalent to vector autoregressive moving average-type models. However, our models are especially useful when the structure of the graph, associated with the multivariate time series, changes over time. Such network topology changes are invisible to standard VARMA-like models. For integrated network time series models we introduce network differencing based on a network lifting (wavelet) transform and remark on some of its properties. We demonstrate our techniques on some real data for some example analysis talks for network time series.