# Robust Sales forecasting Using Deep Learning with Static and Dynamic Covariates
## 1 Introduction  
Accurate sales forecasts are of paramount importance to retailers as they heavily depend on them to effectively manage their supply chains and make crucial decisions related to marketing, logistics, finance, and human resources [1]. Accurate sales forecasts help retailers determine how much inventory they need to purchase from their suppliers in order to meet customer demand. If the forecast is too low, they risk running out of stock and losing sales. If the forecast is too high, they risk overstocking and tying up cash in excess inventory. Sales forecasts also help retailers plan their logistics operations, such as determining how much warehouse space they need, how many trucks they need to transport goods, and how much labor is required to handle incoming and outgoing shipments. They also help retailers plan their marketing campaigns, such as determining which products to promote, which channels to use, and how much to spend on advertising. By having a clear understanding of expected sales volumes, retailers can more effectively allocate their marketing budgets. Accurate sales forecasts are also important for financial planning, such as budgeting and forecasting cash flow. Retailers need to know how much revenue they can expect in order to plan for expenses, investments, and debt repayment. Finally, sales forecasts are used by retailers to plan their staffing needs. They need to know how many employees they will need in their stores and warehouses in order to meet customer demand, and how much labor they will need to handle incoming and outgoing shipments [2]. A global forecasting model, such as a recurrent neural network (RNN), is a model that uses information from multiple time series to make predictions [3; 4]. This is in contrast to a univariate forecasting model like autoregressive integrated moving average (ARIMA) or exponential smoothing (ETS) [5], which only use information from a single time series to make predictions. In a global forecasting model, the RNN is trained on multiple time series at once. Each time series is considered a separate input sequence, and the RNN is trained to capture the patterns and relationships between the different time series. This allows the model to make predictions for all of the time series simultaneously. One advantage of using a global forecasting model like an RNN is that it can capture complex dependencies between the different time series. For example, the sales of one product in a store may be influenced by the sales of a complementary product, or sales at one store may be influenced by sales at nearby stores. By using a global model that takes into account all of the relevant time series, we can better capture these relationships and make more accurate predictions [6]. Another advantage of using a global model is that it can help reduce uncertainty in the individual time series. In some cases, individual time series may be noisy or exhibit erratic behavior. By using a global model that incorporates information from multiple time series, we can reduce the impact of these individual anomalies and improve the overall accuracy of the forecasts [7]. In retail forecasting, covariates (also known as exogenous variables or features) can be used to help improve the accuracy of forecasts [8]. Retail sales can be influenced by the time of year, as well as holidays, weekends, and other special events. Including calendar variables such as the day of week, month, and year can help capture these effects. Changes in price can also have a significant impact on sales. Including variables such as regular price, discount percentage, and promotional price can help capture these effects. Promotions, advertising, and other marketing activities can also influence sales. Including variables such as the type and frequency of marketing activities can help capture these effects. Weather conditions can affect the demand for certain products. Including variables such as temperature, precipitation, and wind speed can help capture these effects.