Sales forecasting for retail or manufacturers should be reconciled at every planning level, such as pairs item-vendor, item-region, or item-group. This alignment can be described by the hierarchy of analytical item attributes. Clearly, when forecasting at the item-store level, we would like the forecasts aggregated to item-region or item-distribution center (DC) to match the actual sales of that item in the region or DC. Forecast reconciling allows for improvement across the entire hierarchy chain.
In this article, we will briefly describe the issue of forecasting items with hierarchical attributes and discuss general approaches to solving this problem.
.

Let’s assume we are forecasting sales for a meat processing company. The total quantity of products sold by the manufacturer can be categorized into items such as beef, pork, and chicken. However, product categorization doesn’t have to stop there. At the top-level groups, we might have broader categories like fresh meat, sausages, delicatessen, and semi-finished products. Within each group, for instance, the ‘sausages’ category, there can be subgroups such as boiled, air-dried, smoked, and so on. Each of these subgroups can further be broken down into more specific attribute categories.
Sales hierarchy can also be defined by geographical features. For example, the overall quantity of sold goods can be segmented by countries, regions, cities, down to distribution channels or individual points of sale. Regional preferences significantly impact the product lineup. In some regions, manufacturers use specific attributes like ‘halal,’ indicating compliance with traditional norms for a significant population group in that area. Regardless, all these attributes are categorical and should be considered during forecasting.
Below, an abstract example of a two-level hierarchical data structure is presented.

Suppose we are calculating for a company that, based on sales forecasts for products in regions A and B, is budgeting for the next year. We have only two regions: one where two products are sold, and the other where three are sold. In this small example, to calculate forecasts for logistics planning, we need to make predictions at all three levels, resulting in a total of 1 + 2 + 5 = 8 forecasts. At the lowest level, there are only 5 forecasts; at the middle level, there are 2; and finally, there’s an additional forecast at the top level.
The forecasts at different levels in this example must adhere to the following condition:
Total = AA + AB + AC + BA + BB
Where:
· A = AA + AB + AC
· B = BA + BB
At first glance, this condition should naturally hold if we forecast the five series at the lowest level, and the other forecasts are obtained through aggregation. However, in practice, this doesn’t always happen. Aggregation can lead to overestimation or underestimation of forecasts at higher levels of the hierarchy.

There are two classical approaches for reconciling forecasts in hierarchical forecasting: the top-down method and the bottom-up method.

1. Top-Down Method: This approach involves forecasting the fully aggregated series and then decomposing the forecasts based on historical proportions. Essentially, you start with a high-level forecast and distribute it down the hierarchy.
2. Bottom-Up Method: In contrast, the bottom-up method entails forecasting each time series at the lowest level of the hierarchy and then using simple aggregation to obtain forecasts at higher levels.

In practice, some companies combine these methods by obtaining forecasts at intermediate hierarchy levels. They then aggregate these forecasts to obtain higher-level forecasts and decompose them to get forecasts at lower levels. However, neither of these methods fully considers the internal correlation structure of the hierarchy, and obtaining prediction intervals from these methods can be challenging.

1. Optimal Approach: An optimal approach involves a two-step process. First, independently forecast all time series at each hierarchy level. Then, reconcile these forecasts according to each level of the hierarchy. Forecast reconciliation minimizes forecasting errors across all hierarchy levels. This approach offers advantages over the previously described reconciliation methods."

Hierarchical forecasting is a powerful tool for data management and analysis, allowing effective modeling and prediction of sales at different levels of hierarchy. Here are several key reasons why this approach is important:
1. Forecast Reconciliation Across Levels: For instance, sales data can be organized by countries, regions, product categories, and specific items. To plan logistics effectively, forecasts must be aligned across all analytical dimensions.
2. Improved Forecasting: Hierarchical forecasting considers dependencies between data at different levels. For example, category-level sales forecasts may depend on product-level forecasts, leading to improved accuracy and reduced errors.
3. Optimal Information Utilization: Leveraging information from lower hierarchy levels refines forecasts at higher levels. If we have precise data on specific product sales, we can use it to enhance category-level sales forecasts.
4. Resource Management: Hierarchical forecasting optimizes resource allocation. For production planning, considering forecasts at various levels helps avoid overproduction or shortages.
In summary, hierarchical forecasting enhances forecast accuracy, resource optimization, and provides a structured representation of data.