# Robust Sales forecasting Using Deep Learning with Static and Dynamic Covariates
## 5 Conclusions  
Retailers heavily depend on accurate sales forecasts to effectively manage their supply chains and make informed decisions about purchasing, logistics, marketing, finance, and human resources. An advantage of using a global forecasting model, such as an RNN, is its ability to capture intricate dependencies and relationships between different time series. For instance, the sales of a complementary product can affect the sales of another product in a store, or the sales of a particular store can be influenced by the sales at nearby stores. By utilizing a comprehensive model that incorporates all relevant time series, we can more effectively capture these interrelationships and make more accurate predictions.  
In retail forecasting, covariates such as calendar events, changes in pricing, and weather conditions can be employed to enhance the forecast accuracy. The objective of this study was to examine how the accuracy of global forecasting models is influenced by the inclusion of various possible demand covariates, considering their potential impact on operational decision making. To ensure the significance of our findings, we employed the widely recognized and openly accessible dataset from the M5 competition. We trained DeepAR global models using the complete M5 dataset, which comprises 30,490 product sales across ten stores.  
To assess the significance of the different feature types, we included them both individually and in various combinations, comparing their performance against the baseline case where no features were used. The findings reveal that the DeepAR model, whether with or without additional features, consistently demonstrates a significantly superior performance compared to the univariate seasonal naive benchmark. The inclusion of time, event, and ID-related features consistently enhances the accuracy of the baseline DeepAR model, which lacks any covariates. In general, the inclusion of price-related features does not lead to performance improvements in DeepAR models across various feature combinations. This observation is not surprising, especially in the context of a retailer like Walmart, which follows an \"Everyday Low Prices\" strategy, resulting in relatively stable price distributions. The utility of ID-related features greatly surpasses that of time and event-related features.  
Figure 6: Influence of prices and IDs’ inclusion in DeepAR models. Hollow dots represent errors from models without prices/IDs, while solid dots represent errors from models with prices/IDs.  
However, the best performance is achieved when all three groups of features are used in combination, suggesting that the individual relevance of each feature type is accentuated when information from all sources is considered jointly. Overall, the best-performing model demonstrates a 1.8% improvement in RMSSE and a 6.5% improvement in MASE compared to the model without any additional features.  
Conceptualization, J.M.O. and P.R.; methodology, J.M.O. and P.R.; software, J.M.O. and P.R.; validation, J.M.O. and P.R.; formal analysis, J.M.O. and P.R.; investigation, J.M.O. and P.R.; resources, J.M.O. and P.R.; data curation, J.M.O. and P.R.; writing--original draft preparation, J.M.O. and P.R.; writing--review and editing, J.M.O. and P.R.; visualization, J.M.O. and P.R. All authors have read and agreed to the published version of the manuscript. This research received no external funding.  
A publicly available dataset was used in this study. The data can be found here: [[https://www.kaggle.com/competitions/m5-forecasting-accuracy/data](https://www.kaggle.com/competitions/m5-forecasting-accuracy/data)]([https://www.kaggle.com/competitions/m5-forecasting-accuracy/data](https://www.kaggle.com/competitions/m5-forecasting-accuracy/data)) (accessed on 6 January 2023).  
The authors declare no conflicts of interest.