Understanding Hierarchy Reconciliation

When data is organized in a hierarchical fashion, there are often accounting constraints that link the data at different levels of the hierarchy. Typically, for any historical time period, the data in a parent node is either the sum or the average of the data of its child nodes. For example, the total sales of a product by a retail company is the sum of the sales of the same product in all stores that belong to the company. With forecasta numerical prediction of a future value for a specified time period for each unique combination of BY variable values data, however, time seriesan aggregation of transactional data into specified time intervals and sorted according to unique combinations of the default attributes (BY variables) are often forecast independently at different levels. As a result, the forecast values do not abide by the constraints that bind the original series. However, you can enforce these constraints by using an after-the-fact process known as reconciliation of hierarchical forecasts. In the hierarchical model, you can select from these reconciliation methods:

Top-down

aggregates the data from the lowest level to each higher level, including the highest level, and then uses the aggregated data to generate the forecasts at all levels. SAS Visual Forecasting then performs the reconciliation, starting at the highest level, by disaggregating each level's forecasts to the level below it by using your specified disaggregation methoda method that specifies how the forecasts in the lower level of the hierarchy are reconciled when the reconciliation method is top-down or middle-out. The disaggregation method can reconcile the forecasts in either of the following ways: (1) by using the proportion that each lower-level forecast contributes to the higher-level forecast; or (2) by splitting equally the difference between the higher-level forecast and the lower-level forecasts..

You can specify one of the following disaggregation methods:

• Difference - bases the loss function on the root mean square error (RMSE), which results in adjustments that are the (possibly weighted) mean difference of the aggregated child nodes and the parent node.
• Proportions - uses a loss function that results in reconciled forecasts that are the (possibly weighted) proportional disaggregation of the parent node.

The top-down method enables you to remove the excessive noise from the data at the lower levels of the hierarchy. However, you also might lose some components of the pattern (such as the seasonalitya regular change in time series data values that occurs at the same point in each time cycle.) in the forecast.

Bottom-Up

uses the data at the lowest level of the hierarchy to generate the forecasts at the lowest level. The reconciliation process then aggregates these forecasts to the higher levels in the hierarchy.

The bottom-up method enables you to see any patterns (such as seasonality) in the data. However, because you are using the lowest level of the hierarchy as a reference level for the forecasts, you can also have too much noise or randomness in the data. Also, these forecasts might fail because the data at the lowest level of the hierarchy can be sporadic or too sparse.

Middle-out

aggregates the data from the lowest level to each higher level, up to the middle level, and then uses the aggregated data to generate the forecasts at the middle level and all levels below the middle level. The reconciliation process aggregates the forecasts of the middle level to the levels higher than the middle level and disaggregates the forecasts of each level, starting at the middle level, to the level below it by using your specified disaggregation method.

The following example shows how the forecasts are generated for the hierarchy Region > Product Category > Product Line > Product, based on the reconciliation methodthe method that specifies the level in the hierarchy where the process of reconciliation starts. The following reconciliation methods are available: bottom-up method, middle-out method, and top-down method. that you choose. Aggregation forecasts for the higher levels in the hierarchy are created based on the aggregationthe process of combining more than one time series to form a single series within the same time interval. For example, data can be combined into a total or an average. statistic that you select. Disaggregation forecasts for the lower levels in the hierarchy are created based on the disaggregation method that you select.