  Identifying the topology underlying a set of time series is useful for tasks
such as prediction, denoising, and data completion. Vector autoregressive (VAR)
model-based topologies capture dependencies among time series and are often
inferred from observed spatio-temporal data. When data are affected by noise
and/or missing samples, topology identification and signal recovery
(reconstruction) tasks must be performed jointly. Additional challenges arise
when i) the underlying topology is time-varying, ii) data become available
sequentially, and iii) no delay is tolerated. This study proposes an online
algorithm to overcome these challenges in estimating VAR model-based
topologies, having constant complexity per iteration, which makes it
interesting for big-data scenarios. The inexact proximal online gradient
descent framework is used to derive a performance guarantee for the proposed
algorithm, in the form of a dynamic regret bound. Numerical tests are also
presented, showing the ability of the proposed algorithm to track time-varying
topologies with missing data in an online fashion.
