Version 1
: Received: 19 September 2023 / Approved: 20 September 2023 / Online: 10 October 2023 (13:23:25 CEST)
Version 2
: Received: 13 October 2023 / Approved: 16 October 2023 / Online: 16 October 2023 (16:59:16 CEST)
Version 3
: Received: 23 October 2023 / Approved: 24 October 2023 / Online: 25 October 2023 (13:20:27 CEST)
Kovtun, V.; Giloni, A.; Hurvich, C.; Seshadri, S. Pivot Clustering to Minimize Error in Forecasting Aggregated Demand Streams Each following an Autoregressive Moving Average Model. Stats2023, 6, 1198-1225.
Kovtun, V.; Giloni, A.; Hurvich, C.; Seshadri, S. Pivot Clustering to Minimize Error in Forecasting Aggregated Demand Streams Each following an Autoregressive Moving Average Model. Stats 2023, 6, 1198-1225.
Kovtun, V.; Giloni, A.; Hurvich, C.; Seshadri, S. Pivot Clustering to Minimize Error in Forecasting Aggregated Demand Streams Each following an Autoregressive Moving Average Model. Stats2023, 6, 1198-1225.
Kovtun, V.; Giloni, A.; Hurvich, C.; Seshadri, S. Pivot Clustering to Minimize Error in Forecasting Aggregated Demand Streams Each following an Autoregressive Moving Average Model. Stats 2023, 6, 1198-1225.
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, that we call Pivot Clustering, to create these clusters. We also provide theoretical results to investigate sub-aggregation, including for special cases such as, aggregating MA(1) streams and ARMA streams with similar or same parameters.
Keywords
forecasting aggregate demand; clustering time series; pivot clustering; ARMA model; order-up-to policy
Subject
Business, Economics and Management, Econometrics and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: sridhar seshadri
Commenter's Conflict of Interests: Author