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

Vladimir Kovtun, Avi Giloni, Clifford Hurvich, Sridhar Seshadri

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1198-1225
Number of pages28
JournalStats
Volume6
Issue number4
DOIs
StatePublished - Dec 2023

Keywords

  • forecasting aggregate demand
  • order-up-to policy
  • ARMA model
  • Pivot Clustering
  • clustering time series

ASJC Scopus subject areas

  • Statistics and Probability

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