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

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.