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Optimal combination forecasts for hierarchical time series

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  • Hyndman, Rob J.
  • Ahmed, Roman A.
  • Athanasopoulos, George
  • Shang, Han Lin

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 55 (2011)
Issue (Month): 9 (September)
Pages: 2579-2589

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Handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2579-2589

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Web page: http://www.elsevier.com/locate/csda

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Keywords: Bottom-up forecasting Combining forecasts GLS regression Hierarchical forecasting Reconciling forecasts Top-down forecasting;

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References

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  1. A. Espasa & E. Senra & R. Albacete, 2002. "Forecasting inflation in the European Monetary Union: A disaggregated approach by countries and by sectors," The European Journal of Finance, Taylor & Francis Journals, vol. 8(4), pages 402-421.
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  3. Kohn, Robert, 1982. "When is an aggregate of a time series efficiently forecast by its past?," Journal of Econometrics, Elsevier, vol. 18(3), pages 337-349, April.
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  9. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
  10. Athanasopoulos, George & Ahmed, Roman A. & Hyndman, Rob J., 2009. "Hierarchical forecasts for Australian domestic tourism," International Journal of Forecasting, Elsevier, vol. 25(1), pages 146-166.
  11. Zellner, Arnold & Tobias, Justin, 2004. "A Note on Aggregation, Disaggregation and Forecasting Performance," Staff General Research Papers 12371, Iowa State University, Department of Economics.
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  18. Tian, Yongge & Wiens, Douglas P., 2006. "On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1265-1272, July.
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  1. > Econometrics > Forecasting
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Cited by:
  1. Athanasopoulos, George & Ahmed, Roman A. & Hyndman, Rob J., 2009. "Hierarchical forecasts for Australian domestic tourism," International Journal of Forecasting, Elsevier, vol. 25(1), pages 146-166.
  2. Carlos Capistrán & Christian Constandse & Manuel Ramos Francia, 2009. "Using Seasonal Models to Forecast Short-Run Inflation in Mexico," Working Papers 2009-05, Banco de México.
  3. Medel, Carlos A., 2012. "How informative are in-sample information criteria to forecasting? the case of Chilean GDP," MPRA Paper 35949, University Library of Munich, Germany.
  4. Capistrán, Carlos & Constandse, Christian & Ramos-Francia, Manuel, 2010. "Multi-horizon inflation forecasts using disaggregated data," Economic Modelling, Elsevier, vol. 27(3), pages 666-677, May.
  5. Moon, Seongmin & Simpson, Andrew & Hicks, Christian, 2013. "The development of a classification model for predicting the performance of forecasting methods for naval spare parts demand," International Journal of Production Economics, Elsevier, vol. 143(2), pages 449-454.
  6. Moon, Seongmin & Hicks, Christian & Simpson, Andrew, 2012. "The development of a hierarchical forecasting method for predicting spare parts demand in the South Korean Navy—A case study," International Journal of Production Economics, Elsevier, vol. 140(2), pages 794-802.
  7. Sbrana, Giacomo & Silvestrini, Andrea, 2013. "Forecasting aggregate demand: Analytical comparison of top-down and bottom-up approaches in a multivariate exponential smoothing framework," International Journal of Production Economics, Elsevier, vol. 146(1), pages 185-198.

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