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Pivot Clustering to Minimize Error in Forecasting Aggregated Demand Streams Each Following an Autoregressive Moving Average Model

Author

Listed:
  • Vladimir Kovtun

    (Sy Syms School of Business, Yeshiva University, Suite 334, 215 Lexington Avenue, New York, NY 10012, USA)

  • Avi Giloni

    (Sy Syms School of Business, Yeshiva University, BH-428, 500 West 185th St., New York, NY 10033, USA)

  • Clifford Hurvich

    (Technology, Operations and Statistics, Leonard N. Stern School of Business, New York University, 44 West 4th St., New York, NY 10012, USA)

  • Sridhar Seshadri

    (Gies College of Business and Carle Illinois College of Medicine, University of Illinois at Urbana-Champaign, 601 E John Street, Champaign, IL 61820, USA)

Abstract

In this paper, we compare the effects of forecasting demand using individual (disaggregated) components versus first aggregating the components either fully or into several clusters. Demand streams are assumed to follow autoregressive moving average (ARMA) processes. Using individual demand streams will always lead to a superior forecast compared to any aggregates; however, we show that if several aggregated clusters are formed in a structured manner, then these subaggregated clusters will lead to a forecast with minimal increase in mean-squared forecast error. We show this result based on theoretical MSFE obtained directly from the models generating the clusters as well as estimated MSFE obtained directly from simulated demand observations. We suggest a pivot algorithm, which we call Pivot Clustering, to create these clusters. We also provide theoretical results to investigate sub-aggregation, including for special cases, such as aggregating demand generated by MA(1) models and aggregating demand generated by ARMA models with similar or the same parameters.

Suggested Citation

  • Vladimir Kovtun & Avi Giloni & Clifford Hurvich & Sridhar Seshadri, 2023. "Pivot Clustering to Minimize Error in Forecasting Aggregated Demand Streams Each Following an Autoregressive Moving Average Model," Stats, MDPI, vol. 6(4), pages 1-28, November.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:4:p:75-1225:d:1273145
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    References listed on IDEAS

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    1. 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.
    2. Saif Benjaafar & Mohsen ElHafsi & Francis de Véricourt, 2004. "Demand Allocation in Multiple-Product, Multiple-Facility, Make-to-Stock Systems," Management Science, INFORMS, vol. 50(10), pages 1431-1448, October.
    3. Kovtun, Vladimir & Giloni, Avi & Hurvich, Clifford, 2019. "The value of sharing disaggregated information in supply chains," European Journal of Operational Research, Elsevier, vol. 277(2), pages 469-478.
    4. Ma, Shaohui & Fildes, Robert & Huang, Tao, 2016. "Demand forecasting with high dimensional data: The case of SKU retail sales forecasting with intra- and inter-category promotional information," European Journal of Operational Research, Elsevier, vol. 249(1), pages 245-257.
    5. Avi Giloni & Clifford Hurvich & Sridhar Seshadri, 2014. "Forecasting and information sharing in supply chains under ARMA demand," IISE Transactions, Taylor & Francis Journals, vol. 46(1), pages 35-54.
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