Modeling product sales with uncertain differential equation: an application to Meituan

Haoxuan Li (), Jianlin He (), Qi Zhang (), Chuanmei Zhang (), Wusheng Wang (), Xianshuai Cao (), Tongjie Zhang () and Xiangfeng Yang ()
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Haoxuan Li: University of International Business and Economics
Jianlin He: Meituan
Qi Zhang: University of International Business and Economics
Chuanmei Zhang: Meituan
Wusheng Wang: Meituan
Xianshuai Cao: Meituan
Tongjie Zhang: Meituan
Xiangfeng Yang: University of International Business and Economics

Fuzzy Optimization and Decision Making, 2025, vol. 24, issue 2, No 5, 292 pages

Abstract: Abstract Modeling and predicting product sales is pivotal for the sustained growth of firms. Machine learning models often necessitate extensive datasets with diverse features. This requirement poses significant challenges in the case of data scarcity and prevalent missing values. Uncertain differential equations demonstrate enhanced capability in modeling datasets with limited size and offer a good interpretation on product sales fluctuations. Therefore, this study models product sales using uncertain differential equations. Initially, we employ rolling window cross-validation to select the most appropriate uncertain differential equation. Then, parameter estimation is conducted using the least squares method, followed by validation of the fitted uncertain differential equation through an uncertain hypothesis test. Finally, comparisons with alternative models highlight the advantages of the uncertain differential equation on predicting product sales.

Keywords: Sales forecast; Uncertain differential equation; Rolling window cross-validation; Parameter estimation; Uncertain hypothesis test (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10700-025-09446-0

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