Transformer-Based Models for Probabilistic Time Series Forecasting with Explanatory Variables

Ricardo Caetano, José Manuel Oliveira () and Patrícia Ramos
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Ricardo Caetano: ISCAP, Polytechnic of Porto, Rua Jaime Lopes Amorim s/n, 4465-004 São Mamede de Infesta, Portugal
José Manuel Oliveira: Institute for Systems and Computer Engineering, Technology and Science, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Patrícia Ramos: Institute for Systems and Computer Engineering, Technology and Science, Campus da FEUP, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal

Mathematics, 2025, vol. 13, issue 5, 1-29

Abstract: Accurate demand forecasting is essential for retail operations as it directly impacts supply chain efficiency, inventory management, and financial performance. However, forecasting retail time series presents significant challenges due to their irregular patterns, hierarchical structures, and strong dependence on external factors such as promotions, pricing strategies, and socio-economic conditions. This study evaluates the effectiveness of Transformer-based architectures, specifically Vanilla Transformer, Informer, Autoformer, ETSformer, NSTransformer, and Reformer, for probabilistic time series forecasting in retail. A key focus is the integration of explanatory variables, such as calendar-related indicators, selling prices, and socio-economic factors, which play a crucial role in capturing demand fluctuations. This study assesses how incorporating these variables enhances forecast accuracy, addressing a research gap in the comprehensive evaluation of explanatory variables within multiple Transformer-based models. Empirical results, based on the M5 dataset, show that incorporating explanatory variables generally improves forecasting performance. Models leveraging these variables achieve up to 12.4% reduction in Normalized Root Mean Squared Error (NRMSE) and 2.9% improvement in Mean Absolute Scaled Error (MASE) compared to models that rely solely on past sales. Furthermore, probabilistic forecasting enhances decision making by quantifying uncertainty, providing more reliable demand predictions for risk management. These findings underscore the effectiveness of Transformer-based models in retail forecasting and emphasize the importance of integrating domain-specific explanatory variables to achieve more accurate, context-aware predictions in dynamic retail environments.

Keywords: transformers; time series; probabilistic forecasting; retail; covariates; deep learning; data-driven decision making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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