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Optimal Forecast Reconciliation with Time Series Selection

Author

Listed:
  • Xiaoqian Wang
  • Rob J Hyndman
  • Shanika Wickramasuriya

Abstract

Forecast reconciliation ensures forecasts of time series in a hierarchy adhere to aggregation constraints, enabling aligned decision making. While forecast reconciliation can enhance overall accuracy in hierarchical or grouped structures, the most substantial improvements occur in series with initially poor-performing base forecasts. Nevertheless, certain series may experience deteriorations in reconciled forecasts. In practical settings, series in a structure often exhibit poor base forecasts due to model misspecification or low forecastability. To prevent their negative impact, we propose two categories of forecast reconciliation methods that incorporate time series selection based on out-of-sample and in-sample information, respectively. These methods keep "poor" base forecasts unused in forming reconciled forecasts, while adjusting weights allocated to the remaining series accordingly when generating bottom-level reconciled forecasts. Additionally, our methods ameliorate disparities stemming from varied estimates of the base forecast error covariance matrix, alleviating challenges associated with estimator selection. Empirical evaluations through two simulation studies and applications using Australian labour force and domestic tourism data demonstrate improved forecast accuracy, particularly evident in higher aggregation levels, longer forecast horizons, and cases involving model misspecification.

Suggested Citation

  • Xiaoqian Wang & Rob J Hyndman & Shanika Wickramasuriya, 2024. "Optimal Forecast Reconciliation with Time Series Selection," Monash Econometrics and Business Statistics Working Papers 5/24, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2024-5
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/2024/wp05-2024.pdf
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    References listed on IDEAS

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    1. Athanasopoulos, George & Hyndman, Rob J. & Kourentzes, Nikolaos & Panagiotelis, Anastasios, 2024. "Forecast reconciliation: A review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 430-456.
    2. Shanika L. Wickramasuriya & George Athanasopoulos & Rob J. Hyndman, 2019. "Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 804-819, April.
    3. Jian Huang & Shuange Ma & Huiliang Xie & Cun-Hui Zhang, 2009. "A group bridge approach for variable selection," Biometrika, Biometrika Trust, vol. 96(2), pages 339-355.
    4. Panagiotelis, Anastasios & Athanasopoulos, George & Gamakumara, Puwasala & Hyndman, Rob J., 2021. "Forecast reconciliation: A geometric view with new insights on bias correction," International Journal of Forecasting, Elsevier, vol. 37(1), pages 343-359.
    5. 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.
    6. 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.
    7. Hollyman, Ross & Petropoulos, Fotios & Tipping, Michael E., 2021. "Understanding forecast reconciliation," European Journal of Operational Research, Elsevier, vol. 294(1), pages 149-160.
    8. 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.
    9. Zhang, Bohan & Kang, Yanfei & Panagiotelis, Anastasios & Li, Feng, 2023. "Optimal reconciliation with immutable forecasts," European Journal of Operational Research, Elsevier, vol. 308(2), pages 650-660.
    10. Nystrup, Peter & Lindström, Erik & Pinson, Pierre & Madsen, Henrik, 2020. "Temporal hierarchies with autocorrelation for load forecasting," European Journal of Operational Research, Elsevier, vol. 280(3), pages 876-888.
    11. Nystrup, Peter & Lindström, Erik & Møller, Jan K. & Madsen, Henrik, 2021. "Dimensionality reduction in forecasting with temporal hierarchies," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1127-1146.
    12. Di Fonzo, Tommaso & Girolimetto, Daniele, 2023. "Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives," International Journal of Forecasting, Elsevier, vol. 39(1), pages 39-57.
    13. 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).
    14. 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.
    15. Souhaib Ben Taieb & James W. Taylor & Rob J. Hyndman, 2021. "Hierarchical Probabilistic Forecasting of Electricity Demand With Smart Meter Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(533), pages 27-43, March.
    16. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    More about this item

    Keywords

    Forecasting; Hierarchical Time Series; Grouped Time Series; Linear Forecast Reconciliation; Integer Programming;
    All these keywords.

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