  High-dimensional panels of time series arise in many scientific disciplines
such as neuroscience, finance, and macroeconomics. Often, co-movements within
groups of the panel components occur. Extracting these groupings from the data
provides a course-grained description of the complex system in question and can
inform subsequent prediction tasks. We develop a novel methodology to model
such a panel as a restricted vector autoregressive process, where the
coefficient matrix is the weighted adjacency matrix of a stochastic block
model. This network time series model, which we call the Network Informed
Restricted Vector Autoregression (NIRVAR) model, yields a coefficient matrix
that has a sparse block-diagonal structure. We propose an estimation procedure
that embeds each panel component in a low-dimensional latent space and clusters
the embedded points to recover the blocks of the coefficient matrix. Crucially,
the method allows for network-based time series modelling when the underlying
network is unobserved. We derive the bias, consistency and asymptotic normality
of the NIRVAR estimator. Simulation studies suggest that the NIRVAR estimated
embedded points are Gaussian distributed around the ground truth latent
positions. On three applications to finance, macroeconomics, and transportation
systems, NIRVAR outperforms competing factor and network time series models in
terms of out-of-sample prediction.
