Quasi-Stationary Promotion Modeling: Measuring the Lifespan and Effectiveness of Marketing Promotions

<ns3:p>Background Promotions in consumer packaged goods (CPG) markets are inherently transient. Each campaign, be it a temporary price reduction (TPR), feature advertisement, in-store display, or combined feature and display, produces an immediate surge in sales followed by an eventual decline once the event ends. Despite this, sales patterns during the active promotional phase often exhibit conditional stability. Methods We introduce a quasi-stationary promotion modeling framework that applies quasi-stationary distributions (QSDs) to characterize the conditional behavior of promotional sales prior to termination. By treating the end of a promotion as an absorbing state and the underlying mechanics (TPR, Feature, Display, and Feature + Display) as transient states, we model the system as a finite-state Markov process. The left eigenvector of the transition sub-matrix yields the conditional sales mix m , while the dominant eigenvalue provides the decay rate α governing promotional persistence. Using simulated 104 -week UPC-level data, we estimate transition probabilities, derive QSD parameters, and analyze promotion lifespans. Results The QSD-based framework quantifies both the effective duration of promotions (via α and 1 / α ) and the relative dominance of different promotional tactics during the active phase (via m ). In simulated CPG settings, the approach differentiates between long-lived and fast-decaying promotions and reveals how transitions among TPR, Feature, Display, and Feature + Display shape conditional sales composition while the promotion is still live. Conclusions Quasi-stationary promotion modeling provides a unified stochastic basis for understanding promotion dynamics, forecasting lift persistence, and optimizing campaign duration. By linking QSD theory with applied decision intelligence in CPG analytics, the framework offers interpretable parameters that can be embedded into promotion planning, portfolio management, and real-time decision systems.</ns3:p>