Minimal Example of Hierarchical ReconciliationLarge collections of time series organized into structures at different aggregation levels often require their forecasts to follow their aggregation constraints, which poses the challenge of creating novel algorithms capable of coherent forecasts. The
HierarchicalForecast package provides a wide collection of Python
implementations of hierarchical forecasting algorithms that follow
classic hierarchical reconciliation.
In this notebook we will show how to use the StatsForecast library to
produce base forecasts, and use HierarchicalForecast package to
perform hierarchical reconciliation.
You can run these experiments using CPU or GPU with Google Colab.
1. Libraries
2. Load Data
In this example we will use theTourismSmall dataset. The following
cell gets the time series for the different levels in the hierarchy, the
summing matrix S which recovers the full dataset from the bottom level
hierarchy and the indices of each hierarchy denoted by tags.
3. Base forecasts
The following cell computes the base forecast for each time series using theauto_arima and naive models. Observe that Y_hat_df
contains the forecasts but they are not coherent.
4. Hierarchical reconciliation
The following cell makes the previous forecasts coherent using theHierarchicalReconciliation class. The used methods to make the
forecasts coherent are:
BottomUp: The reconciliation of the method is a simple addition to the upper levels.TopDown: The second method constrains the base-level predictions to the top-most aggregate-level serie and then distributes it to the disaggregate series through the use of proportions.MiddleOut: Anchors the base predictions in a middle level.
4.1 Coherence Diagnostics
Thereconcile method supports an optional diagnostics=True parameter
that computes a detailed report showing how reconciliation changed the
forecasts. This is useful for:
- Verifying that base forecasts were incoherent and reconciliation fixed them
- Understanding which hierarchy levels were adjusted the most
- Detecting if reconciliation introduced negative values
- Confirming numerical coherence within tolerance
hrec.diagnostics as a DataFrame with
metrics per hierarchical level:
Key metrics explained:
coherence_residual_mae_before: Mean absolute incoherence in base forecasts (should be > 0 if base forecasts are incoherent)coherence_residual_mae_after: Mean absolute incoherence after reconciliation (should be ~0)adjustment_mae/rmse/max: How much forecasts were adjusted by reconciliationnegative_count_before/after: Count of negative forecast valuesis_coherent: Whether the reconciled forecasts satisfy the hierarchical constraints (1.0 = yes)
We can also see which levels required the largest adjustments:
5. Evaluation
TheHierarchicalForecast package includes the evaluate function to
evaluate the different hierarchies and we can use utilsforecast to
compute the mean absolute error relative to a baseline model.
References
- Orcutt, G.H., Watts, H.W., & Edwards, J.B.(1968). Data aggregation and information loss. The American Economic Review, 58 , 773(787).
- Disaggregation methods to expedite product line forecasting.
Journal of Forecasting, 9 , 233–254.
doi:10.1002/for.3980090304.
- An investigation of aggregate variable time series forecast strategies with specific subaggregate time series statistical correlation. Computers and Operations Research, 26 , 1133–1149. doi:10.1016/S0305-0548(99)00017-9.
- Hyndman, R.J., & Athanasopoulos, G. (2021). “Forecasting: principles and practice, 3rd edition: Chapter 11: Forecasting hierarchical and grouped series.”. OTexts: Melbourne, Australia. OTexts.com/fpp3 Accessed on July 2022.