陈佳，英国约克大学

We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over time. Two types of time-varying graphs are investigated: one containing directed edges of Granger causality linkages, and the other containing undirected edges of partial correlation linkages. Under the sparse structural assumption, we propose a penalised local linear method with time-varying weighted group LASSO to jointly estimate the transition matrices and identify their significant entries, and a time-varying CLIME method to estimate the precision matrices. The estimated transition and precision matrices are then used to determine the time-varying network structures. Under some mild conditions, we derive the theoretical properties of the proposed estimates including the consistency and oracle properties. In addition, the developed methodology and theory are extended to highly correlated large-scale time series, for which the sparsity assumption becomes invalid and factor-adjusted time-varying networks are estimated. Extensive simulation studies and an empirical application to a large U.S. macroeconomic dataset are provided to illustrate the finite-sample performance of the developed methods.