A Multi-Layered Algorithmic for Predicting Purchase-Trend Diffusion Across Socioeconomic Strata via Individual Capital-Flow Signatures

Résumé

The prediction of consumer purchasing behaviour has long been approached through aggregate demand functions, demographic segmentation, and survey-based intent modelling, each of which treats the purchasing unit as a static label rather than a dynamic capital-flow entity.This paper proposes the Capital-Pulse Behavioral Model (CPBM), a four-layer algorithmic architecture that reframes every individual in a target community as a micro-pulse station: a continuously emitting financial signal whose seven-dimensional signature encodes purchase frequency, expenditure share, timing entropy, point-specific price elasticity, and cross-category compensation.The individual signatures are aggregated through a graph-diffusion layer whose dynamics follow a modified reaction-diffusion partial differential equation, capturing the social propagation of purchase decisions as a physical wave phenomenon rather than a probabilistic survey outcome.A stratified Bass-model layer then quantifies the inter-stratum temporal lag τ -the delay between peak adoption in a higher socioeconomic stratum and onset growth in the next lower one -thereby producing an actionable marketing timing window.A hybrid predictive engine combining gradient-boosted trees, long short-term memory networks, and graph neural networks fuses all upstream signals into a three-dimensional probability tensor indexed by individual, price tier, and forecast horizon.A synthetic community experiment (N = 500, three strata, sixty-day diffusion horizon) yields an AUC of 0.847, with diffusion peak identified at day 23 and a stratum-3 base purchase rate of 60.8%.The framework is designed for exponential geographic scaling: local community parameters (Neighbourhood Purchasing Inertia I NPI , diffusion coefficient D, and lag τ ) become inputs to a regional model, which in turn feeds a national layer, enabling data-efficient upward aggregation without full model reconstruction.All code is publicly available at the repositories listed above.

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