## 1 Introduction  
The retail sector dominates a big proportion of the service industry in modern countries because it provides a variety of the goods necessary for daily consumption [1, 2]. Generally, retail chains consist of four specific systems: department stores, hypermarkets, supermarkets, and convenience stores. Specifically, households are the primary customers for hypermarkets and supermarkets, while individuals are the primary customers for department stores and convenience stores. Clearly, the product categories, geographical locations, area sizes, and make-up of the main customers are quite different between portions of the retail sector [3, 4, 5]. In practice, the aggregate sales number is the best representative of consumer shopping, pricing policy, promotion plan, and product strategy performance. Inspired by the concept of business analytics, this research highlights three critical issues: sales forecasting (predictive analytics), market analysis (diagnostic analytics), and performance assessment (prescriptive analytics). For the retail sector, sales forecasting helps managers understand customers' behaviors and predict their future desires [6]. Then, a firm can optimize storage space, shelf space, and display space to prepare inventories and develop product strategies. Although sales forecasting is critically important, it is extremely challenging due to the lack of any systematic approaches useful for identifying representative or effective predictors. In sales forecasting, most past studies predict sales by relying on historical data without considering the impacts of the predictors. In particular, significant economic indicators can vary between different portions of the retail sector, or between individual firms [7; 8; 9]. Economic indicators are generally drawn from one of the three categories: leading, lagging, or coincident indicators [10; 11; 12; 13]. Industrial production index (IPI), consumer confidence index (CCI), and purchase manager index (PMI), are usually the leading indicators used in the forecasting of a country's economy [13; 14]. Gross national product (GNP), consumer price index (CPI), producer price index (PPI), and unemployment rates are usually treated as lagging indicators because they can be used to justify economic conditions. Coincident indicators, such as gross domestic product (GDP), personal consumption expenditure (PCE), and regular wage, are concurrent with changes in the economy. In practice, it is not easy to justify the temporal causality (leading, lagging, or coincident) of the indicators. Thus, they are mixed together in this research. Additionally, market competition is very common in the retail sector [15; 16]. Generally, market competition has three types. The first is horizontal competition, meaning competition between homogeneous firms targeting similar segments. The second is vertical competition between the upstream supplier and the downstream retailer. The third is channel competition between online platforms and onsite stores. In reality, the degree of competition depends on the dependences of the interactive firms as related to market segments, customer groups, and product categories [17]. Horizontal competition means that competing firms offer substitutive products or services [18; 19] while vertical competition means that each partner takes a slice of the value chain, similar to profit sharing [12; 20]. Today, artificial intelligence and computer vision have blurred the boundary between online platforms and onsite retailers. Walmart merged an e-commerce platform in 2018, while Amazon opened cashier-less stores the same year. Clearly, channel competition between Amazon and Walmart has become much more intense than it was before. This research focuses on a mix of horizontal and vertical competition between Walmart, Costco, and Kroger. Among them, Walmart provides varieties of products ranging from electronic appliances, furniture, office supplies, sport supplies, and clothes, to fresh food.