Abstract
This study investigates the effectiveness of Transformer-based models for retail demand forecasting. We evaluated vanilla Transformer, Informer, Autoformer, PatchTST, and temporal fusion Transformer (TFT) against traditional baselines like AutoARIMA and AutoETS. Model performance was assessed using mean absolute scaled error (MASE) and weighted quantile loss (WQL). The M5 competition dataset, comprising 30,490 time series from 10 stores, served as the evaluation benchmark. The results demonstrate that Transformer-based models significantly outperform traditional baselines, with Transformer, Informer, and TFT leading the performance metrics. These models achieved MASE improvements of 26% to 29% and WQL reductions of up to 34% compared to the seasonal Na & iuml;ve method, particularly excelling in short-term forecasts. While Autoformer and PatchTST also surpassed traditional methods, their performance was slightly lower, indicating the potential for further tuning. Additionally, this study highlights a trade-off between model complexity and computational efficiency, with Transformer models, though computationally intensive, offering superior forecasting accuracy compared to the significantly slower traditional models like AutoARIMA. These findings underscore the potential of Transformer-based approaches for enhancing retail demand forecasting, provided the computational demands are managed effectively.

Abstract
Retailers depend on accurate sales forecasts to effectively plan operations and manage supply chains. These forecasts are needed across various levels of aggregation, making hierarchical forecasting methods essential for the retail industry. As competition intensifies, the use of promotions has become a widespread strategy, significantly impacting consumer purchasing behavior. This study seeks to improve forecast accuracy by incorporating promotional data into hierarchical forecasting models. Using a sales dataset from a major Portuguese retailer, base forecasts are generated for different hierarchical levels using ARIMA models and Multi-Layer Perceptron (MLP) neural networks. Reconciliation methods including bottom-up, top-down, and optimal reconciliation with OLS and WLS (struct) estimators are employed. The results show that MLPs outperform ARIMA models for forecast horizons longer than one day. While the addition of regressors enhances ARIMA’s accuracy, it does not yield similar improvements for MLP. MLPs present a compelling balance of simplicity and efficiency, outperforming ARIMA in flexibility while offering faster training times and lower computational demands compared to more complex deep learning models, making them highly suitable for practical retail forecasting applications.

Abstract
Retailers depend on accurate forecasts of product sales at the Store x SKU level to efficiently manage their inventory. Consequently, there has been increasing interest in identifying more advanced statistical techniques that lead to accuracy improvements. However, the inclusion of multiple drivers affecting demand into commonly used ARIMA and ETS models is not straightforward, particularly when many explanatory variables are available. Moreover, regularization regression models that shrink the model's parameters allow for the inclusion of a lot of relevant information but do not intrinsically handle the dynamics of the demand. These problems have not been addressed by previous studies. Nevertheless, multiple simultaneous effects interacting are common in retailing. To be successful, any approach needs to be automatic, robust and efficiently scaleable. In this study, we design novel approaches to forecast retailer product sales taking into account the main drivers which affect SKU demand at store level. To address the variable selection challenge, the use of dimensionality reduction via principal components analysis (PCA) and shrinkage estimators was investigated. The empirical results, using a case study of supermarket sales in Portugal, show that both PCA and shrinkage are useful and result in gains in forecast accuracy in the order of 10% over benchmarks while offering insights on the impact of promotions. Focusing on the promotional periods, PCA-based models perform strongly, while shrinkage estimators over-shrink. For the non-promotional periods, shrinkage estimators significantly outperform the alternatives.

Abstract
Global models have been developed to tackle the challenge of forecasting sets of series that are related or share similarities, but they have not been developed for heterogeneous datasets. Various methods of partitioning by relatedness have been introduced to enhance the similarities of sets, resulting in improved forecasting accuracy but often at the cost of a reduced sample size, which could be harmful. To shed light on how the relatedness between series impacts the effectiveness of global models in real-world demand-forecasting problems, we perform an extensive empirical study using the M5 competition dataset. We examine cross-learning scenarios driven by the product hierarchy commonly employed in retail planning to allow global models to capture interdependencies across products and regions more effectively. Our findings show that global models outperform state-of-the-art local benchmarks by a considerable margin, indicating that they are not inherently more limited than local models and can handle unrelated time-series data effectively. The accuracy of data-partitioning approaches increases as the sizes of the data pools and the models' complexity decrease. However, there is a trade-off between data availability and data relatedness. Smaller data pools lead to increased similarity among time series, making it easier to capture cross-product and cross-region dependencies, but this comes at the cost of a reduced sample, which may not be beneficial. Finally, it is worth noting that the successful implementation of global models for heterogeneous datasets can significantly impact forecasting practice.

Abstract
Sales forecasts are an important tool for inventory management, allowing retailers to balance inventory levels with customer demand and market conditions. By using sales forecasts to inform inventory management decisions, companies can optimize their inventory levels and avoid costly stockouts or excess inventory costs. The scale of the forecasting problem in the retail domain is significant and requires ongoing attention and resources to ensure accurate and effective forecasting. Recent advances in machine learning algorithms such as deep learning have made possible to build more sophisticated forecasting models that can learn from large amounts of data. These global models can capture complex patterns and relationships in the data and predict demand across multiple regions and product categories. In this paper, we investigate the cross-learning scenarios, inspired by the product hierarchy frequently utilized in retail planning, which enable global models to better capture interdependencies between different products and regions. Our empirical results obtained using M5 competition dataset indicate that the cross-learning approaches exhibit significantly superior performance compared to local forecasting benchmarks. Our findings also suggest that using partial pooling at the lowest aggregation level of the retail hierarchical allows for a more effective capture of the distinct characteristics of each group.