Hierarchical Forecast 👑

Large 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.

HierarchicalForecast offers a collection of cross-sectional and temporal reconciliation methods, including BottomUp, TopDown, MiddleOut, MinTrace and ERM, as well as probabilistic coherent predictions including Normality, Bootstrap, and PERMBU.

🎊 Features

• Classic reconciliation methods:
  • BottomUp: Simple addition to the upper levels.
  • TopDown: Distributes the top levels forecasts trough the hierarchies.
• Alternative reconciliation methods:
  • MiddleOut: It anchors the base predictions in a middle level. The levels above the base predictions use the bottom-up approach, while the levels below use a top-down.
  • MinTrace: Minimizes the total forecast variance of the space of coherent forecasts, with the Minimum Trace reconciliation.
  • ERM: Optimizes the reconciliation matrix minimizing an L1 regularized objective.
• Probabilistic coherent methods:
  • Normality: Uses MinTrace variance-covariance closed form matrix under a normality assumption.
  • Bootstrap: Generates distribution of hierarchically reconciled predictions using Gamakumara’s bootstrap approach.
  • PERMBU: Reconciles independent sample predictions by reinjecting multivariate dependence with estimated rank permutation copulas, and performing a Bottom-Up aggregation.
• Temporal reconciliation methods:
  • All reconciliation methods (except for the insample methods) are available to use with temporal hierarchies too.

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📖 Why?

Short: We want to contribute to the ML field by providing reliable baselines and benchmarks for hierarchical forecasting task in industry and academia. Here’s the complete paper.

Verbose: HierarchicalForecast integrates publicly available processed datasets, evaluation metrics, and a curated set of statistical baselines. In this library we provide usage examples and references to extensive experiments where we showcase the baseline’s use and evaluate the accuracy of their predictions. With this work, we hope to contribute to Machine Learning forecasting by bridging the gap to statistical and econometric modeling, as well as providing tools for the development of novel hierarchical forecasting algorithms rooted in a thorough comparison of these well-established models. We intend to continue maintaining and increasing the repository, promoting collaboration across the forecasting community.

💻 Installation

PyPI

We recommend using uv as Python package manager, for which you can find installation instructions here.

You can then install the released version of HierachicalForecast:

uv pip install hierarchicalforecast

Alternatively, you can directly install from the Python package index with:

pip install hierarchicalforecast

(Installing inside a python virtualenvironment is recommended.)

Conda

Also you can install the released version of HierarchicalForecast from conda with:

conda install -c conda-forge hierarchicalforecast

(Installing inside a python virtualenvironment or a conda environment is recommended.)

Dev Mode

If you want to make some modifications to the code and see the effects in real time (without reinstalling), follow the steps here.

🧬 How to use

The following example needs statsforecast and datasetsforecast as additional packages. If not installed, install it via your preferred method, e.g. pip install statsforecast datasetsforecast. The datasetsforecast library allows us to download hierarhical datasets and we will use statsforecast to compute base forecasts to be reconciled.

You can open this example in Colab

import pandas as pd

#obtain hierarchical dataset
from datasetsforecast.hierarchical import HierarchicalData

# compute base forecast no coherent
from statsforecast.core import StatsForecast
from statsforecast.models import AutoARIMA, Naive

#obtain hierarchical reconciliation methods and evaluation
from hierarchicalforecast.core import HierarchicalReconciliation
from hierarchicalforecast.evaluation import evaluate
from hierarchicalforecast.methods import BottomUp, TopDown, MiddleOut
from utilsforecast.losses import mse

# Load TourismSmall dataset
Y_df, S_df, tags = HierarchicalData.load('./data', 'TourismSmall')
Y_df['ds'] = pd.to_datetime(Y_df['ds'])
S_df = S_df.reset_index(names="unique_id")

#split train/test sets
Y_test_df  = Y_df.groupby('unique_id').tail(4)
Y_train_df = Y_df.drop(Y_test_df.index)

# Compute base auto-ARIMA predictions
fcst = StatsForecast(models=[AutoARIMA(season_length=4), Naive()],
                     freq='QE', n_jobs=-1)
Y_hat_df = fcst.forecast(df=Y_train_df, h=4)

# Reconcile the base predictions
reconcilers = [
    BottomUp(),
    TopDown(method='forecast_proportions'),
    MiddleOut(middle_level='Country/Purpose/State',
              top_down_method='forecast_proportions')
]
hrec = HierarchicalReconciliation(reconcilers=reconcilers)
Y_rec_df = hrec.reconcile(Y_hat_df=Y_hat_df, Y_df=Y_train_df,
                          S_df=S_df, tags=tags)

Evaluation

df = Y_rec_df.merge(Y_test_df, on=['unique_id', 'ds'], how='left')

evaluate(df=df, metrics=[mse],
                   tags=tags, benchmark='Naive')

How to cite

Here’s the complete paper.

@article{olivares2022hierarchicalforecast,
    author    = {Kin G. Olivares and
                 Federico Garza and 
                 David Luo and 
                 Cristian Challú and
                 Max Mergenthaler and
                 Souhaib Ben Taieb and
                 Shanika L. Wickramasuriya and
                 Artur Dubrawski},
    title     = {{HierarchicalForecast}: A Reference Framework for Hierarchical Forecasting in Python},
    journal   = {Work in progress paper, submitted to Journal of Machine Learning Research.},
    volume    = {abs/2207.03517},
    year      = {2022},
    url       = {https://arxiv.org/abs/2207.03517},
    archivePrefix = {arXiv}
}