  Forecast reconciliation has attracted significant research interest in recent
years, with most studies taking the hierarchy of time series as given. We
extend existing work that uses time series clustering to construct hierarchies,
with the goal of improving forecast accuracy, in three ways. First, we
investigate multiple approaches to clustering, including not only different
clustering algorithms, but also the way time series are represented and how
distance between time series is defined. We find that cluster-based hierarchies
lead to improvements in forecast accuracy relative to two-level hierarchies.
Second, we devise an approach based on random permutation of hierarchies,
keeping the structure of the hierarchy fixed, while time series are randomly
allocated to clusters. In doing so, we find that improvements in forecast
accuracy that accrue from using clustering do not arise from grouping together
similar series but from the structure of the hierarchy. Third, we propose an
approach based on averaging forecasts across hierarchies constructed using
different clustering methods, that is shown to outperform any single clustering
method. All analysis is carried out on two benchmark datasets and a simulated
dataset. Our findings provide new insights into the role of hierarchy
construction in forecast reconciliation and offer valuable guidance on
forecasting practice.
