Title: Stochastic modelling of consumer market volatility: an improved differential equation approach to predicting risk

Authors: Xiang Chen

Addresses: College of Foreign Languages and Economics and Trade, Qingyuan Polytechnic, Qingyuan City, Guangdong Province, 511500, China

Abstract: In macroeconomic operations, consumption behaviour not only reflects the trends of economic variables such as residents' income and market expectations, but also significantly influences policy regulation and industrial adjustment. In the context of increasing global uncertainty, traditional consumption forecasting methods demonstrate limited efficacy in modelling dynamic trajectories and structural fluctuations. This paper proposes a novel consumption fluctuation modelling approach, VAE-SDE, which integrates variational autoencoders (VAE) and stochastic differential equations (SDE). By extracting potential structural information from historical data through the VAE and mapping it to the SDE parameters, the method enables generative forecasting of consumption paths. This approach not only enhances the interpretability of the model but also improves its capacity for uncertainty modelling and path simulation.

Keywords: consumption forecasting; variational autoencoders; VAE; uncertainty modelling; stochastic differential equations; SDE.

DOI: 10.1504/IJDSDE.2025.149963

International Journal of Dynamical Systems and Differential Equations, 2025 Vol.14 No.4, pp.325 - 343

Received: 30 Apr 2025
Accepted: 04 Jul 2025
Published online: 19 Nov 2025 *

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