This project will design new continuous-time NeST models starting from continuous-time network AR and moving average processes and later progressing to more advanced models including multiple network settings. The theoretical properties of such novel models will be developed, and a suitable statistical inference framework will be designed, implemented and tested. Statistical theory currently only exists for basic settings and significant effort is needed for more general ones. This project will interact closely with the related projects in the NeST programme by jointly addressing the challenge of designing methods for dealing with non-stationarities, exogenous variables, local stationarity and long memory.