Time-Varying Generalized Network Autoregressions

We consider a general class of dynamic network autoregressions for high-dimensional time series with network dependence, extending existing dynamic models by allowing for timevarying model coefficients, cross-sectionally dependent errors and a general network structure smoothly evolving along the time. A nonparametric local linear kernel method is proposed to estimate these time-varying coefficients involved, and a recursive-design bootstrap procedure is developed to construct valid confidence intervals for time-varying coefficients in the presence of cross-sectional dependent errors. We establish asymptotic properties for the proposed local-linear based estimator and the bootstrap procedure under mild conditions. Both the proposed estimation and bootstrap procedures are illustrated using simulated and two real datasets. Our work contributes to high-dimensional time series associated with network effects and sheds light on bootstrap inference for locally stationary processes.