# 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 reconciliation methods,
including
`BottomUp`

,
`TopDown`

,
`MiddleOut`

,
`MinTrace`

and
`ERM`

.
And 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.

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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

You can install the *released version* of `HierarchicalForecast`

from
the Python package index with:

```
pip install hierarchicalforecast
```

(Installing inside a python virtualenvironment or a conda environment 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 below:

```
git clone https://github.com/Nixtla/hierarchicalforecast.git
cd hierarchicalforecast
pip install -e .
```

## 🧬 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 numpy as np
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 HierarchicalEvaluation
from hierarchicalforecast.methods import BottomUp, TopDown, MiddleOut
# Load TourismSmall dataset
Y_df, S, tags = HierarchicalData.load('./data', 'TourismSmall')
Y_df['ds'] = pd.to_datetime(Y_df['ds'])
#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(df=Y_train_df,
models=[AutoARIMA(season_length=4), Naive()],
freq='Q', n_jobs=-1)
Y_hat_df = fcst.forecast(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=S, tags=tags)
```

### Evaluation

```
def mse(y, y_hat):
return np.mean((y-y_hat)**2)
evaluator = HierarchicalEvaluation(evaluators=[mse])
evaluator.evaluate(Y_hat_df=Y_rec_df, Y_test=Y_test_df.set_index('unique_id'),
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}
}
```