  This paper discusses the prediction of hierarchical time series, where each
upper-level time series is calculated by summing appropriate lower-level time
series. Forecasts for such hierarchical time series should be coherent, meaning
that the forecast for an upper-level time series equals the sum of forecasts
for corresponding lower-level time series. Previous methods for making coherent
forecasts consist of two phases: first computing base (incoherent) forecasts
and then reconciling those forecasts based on their inherent hierarchical
structure. With the aim of improving time series predictions, we propose a
structured regularization method for completing both phases simultaneously. The
proposed method is based on a prediction model for bottom-level time series and
uses a structured regularization term to incorporate upper-level forecasts into
the prediction model. We also develop a backpropagation algorithm specialized
for application of our method to artificial neural networks for time series
prediction. Experimental results using synthetic and real-world datasets
demonstrate the superiority of our method in terms of prediction accuracy and
computational efficiency.
