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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Bibliographic Details
Published in:Computational statistics & data analysis Vol. 55; no. 9; pp. 2579 - 2589
Main Authors: Hyndman, Rob J., Ahmed, Roman A., Athanasopoulos, George, Shang, Han Lin
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.09.2011
Elsevier
Series:Computational Statistics & Data Analysis
Subjects:
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 Access:Get full text
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Summary: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.
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ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2011.03.006