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Optimal combination forecasts for hierarchical time series

  • Rob J. Hyndman

    ()

  • Roman A. Ahmed

    ()

  • George Athanasopoulos

    ()

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. It also allows us to construct prediction intervals for the resultant forecasts. Finally, we apply the method to forecasting Australian tourism demand where the data are disaggregated by purpose of visit and geographical region.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 9/07.

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Length: 22 pages
Date of creation: Jul 2007
Date of revision:
Handle: RePEc:msh:ebswps:2007-9
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  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.
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  3. Rob J. Hyndman & Yeasmin Khandakar, 2007. "Automatic time series forecasting: the forecast package for R," Monash Econometrics and Business Statistics Working Papers 6/07, Monash University, Department of Econometrics and Business Statistics.
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  11. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2003. "Macroeconomic forecasting in the Euro area: Country specific versus area-wide information," European Economic Review, Elsevier, vol. 47(1), pages 1-18, February.
  12. Solomou, Solomos & Weale, Martin, 1991. "Balanced estimates of UK GDP 1870-1913," Explorations in Economic History, Elsevier, vol. 28(1), pages 54-63, January.
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  14. Weale, Martin, 1985. "Testing Linear Hypotheses on National Account Data," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 685-89, November.
  15. Edwards, John B & Orcutt, Guy H, 1969. "Should Aggregation Prior to Estimation Be the Rule?," The Review of Economics and Statistics, MIT Press, vol. 51(4), pages 409-20, November.
  16. Fair, Ray C & Shiller, Robert J, 1990. "Comparing Information in Forecasts from Econometric Models," American Economic Review, American Economic Association, vol. 80(3), pages 375-89, June.
  17. Tobias, Justin & Zellner, Arnold, 2000. "A Note on Aggregation, Disaggregation and Forecasting Performance," Staff General Research Papers 12024, Iowa State University, Department of Economics.
  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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