Inference of Grouped Time-Varying Network Vector Autoregression Models

This paper considers statistical inference of time-varying network vector autoregression models for large-scale time series. A latent group structure is imposed on the heterogeneous and node-specific time-varying momentum and network spillover effects so that the number of unknown time-varying coefficients to be estimated can be reduced considerably. A classic agglomerative clustering algorithm with normalized distance matrix estimates is combined with a generalized information criterion to consistently estimate the latent group number and membership. A post-grouping local linear smoothing method is proposed to estimate the group-specific time-varying momentum and network effects, substantially improving the convergence rates of the preliminary estimates which ignore the latent structure. In addition, a post-grouping specification test is conducted to verify the validity of the parametric model assumption for group-specific time-varying coefficient functions, and the asymptotic theory is derived for the test statistic constructed via a kernel weighted quadratic form under the null and alternative hypotheses. Numerical studies including Monte-Carlo simulation and an empirical application to the global trade flow data are presented to examine the finite-sample performance of the developed model and methodology.