This project is being led by Professor Matthew Nunes (University of Bath) and Professor Marina Knight (University of York).

In traditional data analysis, spectral methods have been shown to offer a complementary view to time domain analysis, often elucidating different information by identifying the frequencies or scales at which the important structure or dynamic behaviour occurs. In particular, long-range (persistent) dependence can be more robustly characterised and estimated in the spectral domain, leading to more interpretable analysis. However, whilst recent work has explored time domain approaches to modelling network data, spectral analysis of network-structured time series has to date been lacking. This project aims to create a suite of tools to fill this gap in the network literature encompassing the modelling of processes that display stationary behaviour with potentially both short and long-memory components, as well as estimation and inference frameworks for these components. We anticipate impact to be generated in the following application areas: biology and neuroscience, finance and cybersecurity. 

Current work is focussed on two complementary avenues of research.

Long memory describes data which exhibits strong autocorrelation over a large number of time lags.  The degree of long memory is often characterized by the decay of this dependence, and thus interest lies in estimating the parameter describing the decay.  In our setting the long memory behaviour will appear to different extents in data collected at the nodes of a network.  We are currently extending recent time-domain network time series models to the  include long memory components. This work is being undertaken by NeST-aligned PhD student Chiara Boetti (University of Bath).  Since long memory characterization can be equivalently posed in the spectral domain, the next step of this work will be to investigate whether estimation and inference can be improved with this alternative view of long memory.

In parallel, we are considering spectral domain network time series models with different structures, particularly those which can incorporate flexible intranode dependence.