Factor Network Autoregressions

We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents ("multilayer network"), which are summarized into a smaller number of network matrices ("network factors") through a novel tensor-based principal component approach. We provide consistency results for the estimation of the factors and the coefficients of the FNAR. Our approach combines two different dimension-reduction techniques and can be applied to ultra-high dimensional datasets. In an empirical application, we use the FNAR to investigate the cross-country interdependence of GDP growth rates based on a variety of international trade and financial linkages. The model provides a rich characterization of macroeconomic network effects and exhibits good forecast performance compared to popular dimension-reduction methods.