Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
Computers and Operations Research - Special issue on aggregation and disaggregation in operations research
Algorithm 583: LSQR: Sparse Linear Equations and Least Squares Problems
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Forecasting in hierarchical environments
Proceedings of the 25th International Conference on Scientific and Statistical Database Management
Efficient forecasting for hierarchical time series
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
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In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these ''hierarchical time series''. They are commonly forecast using either a ''bottom-up'' or a ''top-down'' method. In this paper we propose a new approach to hierarchical forecasting which provides optimal forecasts that are better than forecasts produced by either a top-down or a bottom-up approach. Our method is based on independently forecasting all series at all levels of the hierarchy and then using a regression model to optimally combine and reconcile these forecasts. The resulting revised forecasts add up appropriately across the hierarchy, are unbiased and have minimum variance amongst all combination forecasts under some simple assumptions. We show in a simulation study that our method performs well compared to the top-down approach and the bottom-up method. We demonstrate our proposed method by forecasting Australian tourism demand where the data are disaggregated by purpose of travel and geographical region.