  In this paper, we consider a deterministic online linear regression model
where we allow the responses to be multivariate. To address this problem, we
introduce MultiVAW, a method that extends the well-known Vovk-Azoury-Warmuth
algorithm to the multivariate setting, and show that it also enjoys logarithmic
regret in time. We apply our results to the online hierarchical forecasting
problem and recover an algorithm from this literature as a special case,
allowing us to relax the hypotheses usually made for its analysis.
