Bootstrapping Network Autoregressive Models for Testing Linearity

We develop methodology for network data with special attention to epidemic network spatio-temporal structures. We provide estimation methodology for linear network autoregressive models for both continuous and count multivariate time series. A study of non-linear models for inference under the assumption of known network structure is provided. We propose a family of test statistics for testing linearity of the imposed model. In particular, we compare empirically two bootstrap versions of a supremum-type quasi-score test. Synthetic data are employed to demonstrate the validity of the methodological results. Finally, an epidemic application of the proposed methodology to daily COVID-19 cases detected on province-level geographical network in Italy complements the work.