  Forecast reconciliation has become a prominent topic in recent forecasting
literature, with a primary distinction made between cross-sectional and
temporal hierarchies. This work focuses on temporal hierarchies, such as
aggregating monthly time series data to annual data. We explore the impact of
various forecast reconciliation methods on temporally aggregated ARIMA models,
thereby bridging the fields of hierarchical forecast reconciliation and
temporal aggregation both theoretically and experimentally. Our paper is the
first to theoretically examine the effects of temporal hierarchical forecast
reconciliation, demonstrating that the optimal method aligns with a bottom-up
aggregation approach. To assess the practical implications and performance of
the reconciled forecasts, we conduct a series of simulation studies, confirming
that the findings extend to more complex models. This result helps explain the
strong performance of the bottom-up approach observed in many prior studies.
Finally, we apply our methods to real data examples, where we observe similar
results.
