  We describe a novel method for modeling non-stationary multivariate time
series, with time-varying conditional dependencies represented through dynamic
networks. Our proposed approach combines traditional multi-scale modeling and
network based neighborhood selection, aiming at capturing temporally local
structure in the data while maintaining sparsity of the potential interactions.
Our multi-scale framework is based on recursive dyadic partitioning, which
recursively partitions the temporal axis into finer intervals and allows us to
detect local network structural changes at varying temporal resolutions. The
dynamic neighborhood selection is achieved through penalized likelihood
estimation, where the penalty seeks to limit the number of neighbors used to
model the data. We present theoretical and numerical results describing the
performance of our method, which is motivated and illustrated using task-based
magnetoencephalography (MEG) data in neuroscience.
