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Optimal combination forecasts for hierarchical time series

Author

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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.

Suggested Citation

  • Rob J. Hyndman & Roman A. Ahmed & George Athanasopoulos, 2007. "Optimal combination forecasts for hierarchical time series," Monash Econometrics and Business Statistics Working Papers 9/07, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2007-9
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    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2007/wp9-07.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

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

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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