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Optimal combination forecasts for hierarchical time series

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  • Rob J. Hyndman

    ()

  • Roman A. Ahmed

    ()

  • George Athanasopoulos

    ()

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. 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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Bibliographic Info

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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Keywords: Bottom-up forecasting; combining forecasts; GLS regression; hierarchical forecasting; Moore-Penrose inverse; reconciling forecasts; top-down forecasting.;

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References

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  1. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
  2. Hubrich, Kirstin, 2005. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," International Journal of Forecasting, Elsevier, vol. 21(1), pages 119-136.
  3. Dangerfield, Byron J. & Morris, John S., 1992. "Top-down or bottom-up: Aggregate versus disaggregate extrapolations," International Journal of Forecasting, Elsevier, vol. 8(2), pages 233-241, October.
  4. Solomou, Solomos & Weale, Martin, 1991. "Balanced estimates of UK GDP 1870-1913," Explorations in Economic History, Elsevier, vol. 28(1), pages 54-63, January.
  5. Massimiliano Marcellino & James H. Stock & Mark W. Watson, . "Macroeconomic Forecasting in the Euro Area: Country Specific versus Area-Wide Information," Working Papers 201, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  6. 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.
  7. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
  8. Tobias, Justin & Zellner, Arnold, 2000. "A Note on Aggregation, Disaggregation and Forecasting Performance," Staff General Research Papers 12024, Iowa State University, Department of Economics.
  9. Solomou, S. & Weale, M., 1992. "UK National Income 1920-1938: The Implications of Balanced Estimates," Cambridge Working Papers in Economics 9221, Faculty of Economics, University of Cambridge.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. Rob J. Hyndman & Yeasmin Khandakar, . "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, American Statistical Association, vol. 27(i03).
  15. Tiao, G. C. & Guttman, Irwin, 1980. "Forecasting contemporal aggregates of multiple time series," Journal of Econometrics, Elsevier, vol. 12(2), pages 219-230, February.
  16. 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.
  17. 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.
  18. E. Shlifer & R. W. Wolff, 1979. "Aggregation and Proration in Forecasting," Management Science, INFORMS, vol. 25(6), pages 594-603, June.
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  1. > Econometrics > Forecasting
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
  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. Rob J Hyndman & Alan Lee & Earo Wang, 2014. "Fast computation of reconciled forecasts for hierarchical and grouped time series," Monash Econometrics and Business Statistics Working Papers 17/14, Monash University, Department of Econometrics and Business Statistics.
  8. 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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