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Forecasting hierarchical and grouped time series through trace minimization

Author

Listed:
  • Shanika L Wickramasuriya
  • George Athanasopoulos
  • Rob J Hyndman

Abstract

Large collections of time series often have aggregation constraints due to product or geographical hierarchies. The forecasts for the disaggregated series are usually required to add up exactly to the forecasts of the aggregated series, a constraint known as “aggregate consistency†. The combination forecasts proposed by Hyndman et al. (2011) are based on a Generalized Least Squares (GLS) estimator and require an estimate of the covariance matrix of the reconciliation errors (i.e., the errors that arise due to aggregate inconsistency). We show that this is impossible to estimate in practice due to identifiability conditions.

Suggested Citation

  • Shanika L Wickramasuriya & George Athanasopoulos & Rob J Hyndman, 2015. "Forecasting hierarchical and grouped time series through trace minimization," Monash Econometrics and Business Statistics Working Papers 15/15, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2015-15
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    File URL: http://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp15-15.pdf
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    References listed on IDEAS

    as
    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. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Petropoulos, Fotios, 2017. "Forecasting with temporal hierarchies," European Journal of Operational Research, Elsevier, vol. 262(1), pages 60-74.
    3. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    4. Hyndman, Rob J. & Lee, Alan J. & Wang, Earo, 2016. "Fast computation of reconciled forecasts for hierarchical and grouped time series," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 16-32.
    5. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    6. Hyndman, Rob J. & Ahmed, Roman A. & Athanasopoulos, George & Shang, Han Lin, 2011. "Optimal combination forecasts for hierarchical time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2579-2589, September.
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    Cited by:

    1. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Petropoulos, Fotios, 2017. "Forecasting with temporal hierarchies," European Journal of Operational Research, Elsevier, vol. 262(1), pages 60-74.
    2. Souhaib Ben Taieb & James W. Taylor & Rob J. Hyndman, 2017. "Coherent Probabilistic Forecasts for Hierarchical Time Series," Monash Econometrics and Business Statistics Working Papers 3/17, Monash University, Department of Econometrics and Business Statistics.
    3. Roach, Cameron, 2019. "Reconciled boosted models for GEFCom2017 hierarchical probabilistic load forecasting," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1439-1450.
    4. Colin O. Quinn & George F. Corliss & Richard J. Povinelli, 2024. "Cross-Temporal Hierarchical Forecast Reconciliation of Natural Gas Demand," Energies, MDPI, vol. 17(13), pages 1-18, June.

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    More about this item

    Keywords

    Hierarchical time series; forecasting; reconciliation; contemporaneous error correlation; trace minimization;
    All these keywords.

    JEL classification:

    • 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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