# Robust Sales forecasting Using Deep Learning with Static and Dynamic Covariates
## 3 Empirical Study
### Dataset and Exploratory Analysis
Our findings suggest that special events slightly outsell non-event days in Texas before 2014, while afterward, their sales are similar. In California and Wisconsin, there is a drop in sales around the same time, but here it is from similar sales to lower sales. This pattern appears to be common, starting from 2013. Our analysis of event types is particularly interesting, especially for Wisconsin, where national events result in a considerable adverse effect on sales figures (Figure 4). Additionally, Wisconsin stands alone as the sole state where cultural events experience lower sales figures, particularly when compared to Texas. On the other hand, religious events show a relatively minor but still unfavorable effect in Wisconsin, while sporting events have positive impacts in all three states. Figure 2: Sales per state on SNAP and non-SNAP days. The \"Everyday Low Prices\" policy has been a key driver of Walmart's success, helping the company to establish a strong position in the highly competitive retail industry. The idea behind this policy is to provide customers with affordable pricing on a wide range of products throughout the year, rather than relying on the typical retail model of offering higher prices and occasional sales. By maintaining low prices every day, Walmart aims to attract and retain customers who value affordability and reliability in their shopping experience. Figure 5 depicts overlapping density plots for weekly average price distributions within each category's departments for each year from 2011 to 2016. As expected, the price distributions have remained relatively steady, experiencing only slight increases, likely attributed to inflation. However, distinct variations exist among the categories. On average, Foods items tend to be more affordable compared to Household items, whereas Hobbies items exhibit a broader range of prices, even displaying a secondary peak at lower price points. Within each category, there are also substantial differences. For instance, in the Foods category, department 3 (Foods3 in dark green) does not have a high-price tail. The Hobbies category exhibits the greatest diversity, with both departments displaying wide-ranging distributions. The Hobbies2 department (depicted in light green) showcases a bimodal structure, encompassing almost all items priced below USD 10, whereas the Hobbies1 department (in pink) exhibits notably higher prices. The price distributions in the Household category are quite similar, but the Household2 department (in light green) has a peak at clearly higher prices than the Household1 department (in pink). An interesting  
Figure 4: Median relative sales per state and per event type. Figure 3: Sales per state on event and non-event days. trend is visible in the Hobbies2 department, which becomes increasingly bimodal over time. The second peak at USD 1 is growing in importance, almost reaching the level of the main peak just above USD 2. Meanwhile, the small secondary peak at half a dollar in the Hobbies1 department (in pink) becomes flatter after 2012. Conversely, the Household departments remain very stable, while the Foods category shows small changes such as the relative growth of the USD 1 peak in the Foods1 department. Furthermore, the M5 dataset encompasses details regarding the item ID (ranging from 1 to 3,049), the category ID (Foods, Hobbies, or Household), the department ID (Foods1, Foods2, Foods3, Hobbies1, Hobbies2, Household1, or Household2), the store ID (CA1, CA2, CA3, CA4, TX1, TX2, TX3, WI1, WI2, or WI3), as well as the state ID (CA, TX, or WI) for each individual item.