Optimal combination forecasts for hierarchical time series

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...

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Veröffentlicht in:	Computational statistics & data analysis Jg. 55; H. 9; S. 2579 - 2589
Hauptverfasser:	Hyndman, Rob J., Ahmed, Roman A., Athanasopoulos, George, Shang, Han Lin
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier B.V 01.09.2011 Elsevier
Schriftenreihe:	Computational Statistics & Data Analysis
Schlagworte:	Bottom-up forecasting Bottom-up forecasting Combining forecasts GLS regression Hierarchical forecasting Reconciling forecasts Top-down forecasting Combining forecasts Exact sciences and technology Forecasting General topics Geography GLS regression Hierarchical forecasting Hierarchies Inference from stochastic processes; time series analysis Mathematical models Mathematics Multivariate analysis Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Optimization Probability and statistics Reconciling forecasts Regression Sciences and techniques of general use Statistics Time series Top-down forecasting Bottom-up forecasting Hierarchical forecasting Top-down forecasting GLS regression Reconciling forecasts Combining forecasts Data analysis Covariance analysis Demand forecasting Time series Prediction theory Statistical estimation Stochastic process Statistical simulation Variance analysis Variance Statistical regression Forecasting theory Unbiased estimation Statistical computation Regression model Filtering theory Autocorrelation Method study
ISSN:	0167-9473, 1872-7352
Online-Zugang:	Volltext
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Zusammenfassung:	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.
Bibliographie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0167-9473 1872-7352
DOI:	10.1016/j.csda.2011.03.006