Properties2
| Type | Concept |
| Note created | Feb 17, 2025 |
In hierarchical time series, reconciliation allows us to perform forecasting at different levels of aggregation to then adjust them so that the aggregated sums fit the top-level forecast.
There advantages to forecasting the top level is that general trends will be better captured, while the advantages of low level methods is that different fine-grained series can be fed other regressors to improve its performance.
Forecast reconciliation attempts to find a way to weight low-level forecast in the aggregations so that the total final forecast is built using the information from the underlying forecasts. There are two main approaches:
- Bottom-up, which overthrows the top level forecasts using the aggregation of the lower levels;
- and forecast reconciliation, which uses regression methods like ordinary least squares (OLS) to find a balance between both informations.
In this example, is the summation matrix, that aggregates each of the base forecasts to each respective rows. When using OLS, our target is to find the matrix to weight each of the base forecasts correctly.
Optimal forecast reconciliation relies on the notion that using bottom-up methods will rarely be optimal: counter intuitively, having a good precision at low level does not imply having a good precision when aggregating; error does not have to be symmetrical and can accumulate.