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

Vladimir Kovtun (), Avi Giloni, Clifford Hurvich and Sridhar Seshadri
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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

Stats, 2023, vol. 6, issue 4, 1-28

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.

Keywords: forecasting aggregate demand; clustering time series; Pivot Clustering; ARMA model; order-up-to policy (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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