Geographical Aggregation (Tourism)

Geographical Hierarchical Forecasting on Australian Tourism Data

In many applications, a set of time series is hierarchically organized. Examples include the presence of geographic levels, products, or categories that define different types of aggregations. In such scenarios, forecasters are often required to provide predictions for all disaggregate and aggregate series. A natural desire is for those predictions to be “coherent”, that is, for the bottom series to add up precisely to the forecasts of the aggregated series.

In this notebook we present an example on how to use HierarchicalForecast to produce coherent forecasts between geographical levels. We will use the classic Australian Domestic Tourism (Tourism) dataset, which contains monthly time series of the number of visitors to each state of Australia.

We will first load the Tourism data and produce base forecasts using an AutoETS model from StatsForecast, and then reconciliate the forecasts with several reconciliation algorithms from HierarchicalForecast. Finally, we show the performance is comparable with the results reported by the Forecasting: Principles and Practice which uses the R package fable.

You can run these experiments using CPU or GPU with Google Colab.

!pip install hierarchicalforecast statsforecast

1. Load and Process Data

In this example we will use the Tourism dataset from the Forecasting: Principles and Practice book.

The dataset only contains the time series at the lowest level, so we need to create the time series for all hierarchies.

import numpy as np
import pandas as pd

Y_df = pd.read_csv('https://raw.githubusercontent.com/Nixtla/transfer-learning-time-series/main/datasets/tourism.csv')
Y_df = Y_df.rename({'Trips': 'y', 'Quarter': 'ds'}, axis=1)
Y_df.insert(0, 'Country', 'Australia')
Y_df = Y_df[['Country', 'Region', 'State', 'Purpose', 'ds', 'y']]
Y_df['ds'] = Y_df['ds'].str.replace(r'(\d+) (Q\d)', r'\1-\2', regex=True)
Y_df['ds'] = pd.PeriodIndex(Y_df["ds"], freq='Q').to_timestamp()
Y_df.head()

	Country	Region	State	Purpose	ds	y
0	Australia	Adelaide	South Australia	Business	1998-01-01	135.077690
1	Australia	Adelaide	South Australia	Business	1998-04-01	109.987316
2	Australia	Adelaide	South Australia	Business	1998-07-01	166.034687
3	Australia	Adelaide	South Australia	Business	1998-10-01	127.160464
4	Australia	Adelaide	South Australia	Business	1999-01-01	137.448533

The dataset can be grouped in the following non-strictly hierarchical structure.

spec = [
    ['Country'],
    ['Country', 'State'], 
    ['Country', 'Purpose'], 
    ['Country', 'State', 'Region'], 
    ['Country', 'State', 'Purpose'], 
    ['Country', 'State', 'Region', 'Purpose']
]

Using the aggregate function from HierarchicalForecast we can get the full set of time series.

from hierarchicalforecast.utils import aggregate

Y_df, S_df, tags = aggregate(Y_df, spec)

Y_df.head()

	unique_id	ds	y
0	Australia	1998-01-01	23182.197269
1	Australia	1998-04-01	20323.380067
2	Australia	1998-07-01	19826.640511
3	Australia	1998-10-01	20830.129891
4	Australia	1999-01-01	22087.353380

S_df.iloc[:5, :5]

	unique_id	Australia/ACT/Canberra/Business	Australia/ACT/Canberra/Holiday	Australia/ACT/Canberra/Other	Australia/ACT/Canberra/Visiting
0	Australia	1.0	1.0	1.0	1.0
1	Australia/ACT	1.0	1.0	1.0	1.0
2	Australia/New South Wales	0.0	0.0	0.0	0.0
3	Australia/Northern Territory	0.0	0.0	0.0	0.0
4	Australia/Queensland	0.0	0.0	0.0	0.0

tags['Country/Purpose']

array(['Australia/Business', 'Australia/Holiday', 'Australia/Other',
       'Australia/Visiting'], dtype=object)

Split Train/Test sets

We use the final two years (8 quarters) as test set.

Y_test_df = Y_df.groupby('unique_id', as_index=False).tail(8)
Y_train_df = Y_df.drop(Y_test_df.index)

Y_train_df.groupby('unique_id').size()

unique_id
Australia                                                72
Australia/ACT                                            72
Australia/ACT/Business                                   72
Australia/ACT/Canberra                                   72
Australia/ACT/Canberra/Business                          72
                                                         ..
Australia/Western Australia/Experience Perth/Other       72
Australia/Western Australia/Experience Perth/Visiting    72
Australia/Western Australia/Holiday                      72
Australia/Western Australia/Other                        72
Australia/Western Australia/Visiting                     72
Length: 425, dtype: int64

2. Computing base forecasts

The following cell computes the base forecasts for each time series in Y_df using the ETS model. Observe that Y_hat_df contains the forecasts but they are not coherent.

from statsforecast.models import AutoETS
from statsforecast.core import StatsForecast

fcst = StatsForecast(models=[AutoETS(season_length=4, model='ZZA')], 
                     freq='QS', n_jobs=-1)
Y_hat_df = fcst.forecast(df=Y_train_df, h=8, fitted=True)
Y_fitted_df = fcst.forecast_fitted_values()

3. Reconcile forecasts

The following cell makes the previous forecasts coherent using the HierarchicalReconciliation class. Since the hierarchy structure is not strict, we can’t use methods such as TopDown or MiddleOut. In this example we use BottomUp and MinTrace.

from hierarchicalforecast.methods import BottomUp, MinTrace
from hierarchicalforecast.core import HierarchicalReconciliation

reconcilers = [
    BottomUp(),
    MinTrace(method='mint_shrink'),
    MinTrace(method='ols')
]
hrec = HierarchicalReconciliation(reconcilers=reconcilers)
Y_rec_df = hrec.reconcile(Y_hat_df=Y_hat_df, Y_df=Y_fitted_df, S_df=S_df, tags=tags)

The dataframe Y_rec_df contains the reconciled forecasts.

Y_rec_df.head()

	unique_id	ds	AutoETS	AutoETS/BottomUp	AutoETS/MinTrace_method-mint_shrink	AutoETS/MinTrace_method-ols
0	Australia	2016-01-01	25990.068004	24381.911737	25428.089783	25894.399067
1	Australia	2016-04-01	24458.490282	22903.895964	23914.271400	24357.301898
2	Australia	2016-07-01	23974.055984	22412.265739	23428.462394	23865.910647
3	Australia	2016-10-01	24563.454495	23127.349578	24089.845955	24470.782393
4	Australia	2017-01-01	25990.068004	24518.118006	25545.358678	25901.362283

4. Evaluation

The HierarchicalForecast package includes an evaluate function to evaluate the different hierarchies and also is capable of compute scaled metrics compared to a benchmark model.

from hierarchicalforecast.evaluation import evaluate
from utilsforecast.losses import rmse, mase
from functools import partial

eval_tags = {}
eval_tags['Total'] = tags['Country']
eval_tags['Purpose'] = tags['Country/Purpose']
eval_tags['State'] = tags['Country/State']
eval_tags['Regions'] = tags['Country/State/Region']
eval_tags['Bottom'] = tags['Country/State/Region/Purpose']

df = Y_rec_df.merge(Y_test_df, on=['unique_id', 'ds'])
evaluation = evaluate(df = df,
                      tags = eval_tags,
                      train_df = Y_train_df,
                      metrics = [rmse,
                                 partial(mase, seasonality=4)])

evaluation.columns = ['level', 'metric', 'Base', 'BottomUp', 'MinTrace(mint_shrink)', 'MinTrace(ols)']
numeric_cols = evaluation.select_dtypes(include="number").columns
evaluation[numeric_cols] = evaluation[numeric_cols].map('{:.2f}'.format).astype(np.float64)

RMSE

The following table shows the performance measured using RMSE across levels for each reconciliation method.

evaluation.query('metric == "rmse"')

	level	metric	Base	BottomUp	MinTrace(mint_shrink)	MinTrace(ols)
0	Total	rmse	1743.29	3028.62	2112.73	1818.94
2	Purpose	rmse	534.75	791.19	577.14	515.53
4	State	rmse	308.15	413.39	316.82	287.32
6	Regions	rmse	51.66	55.13	46.55	46.28
8	Bottom	rmse	19.37	19.37	17.80	18.19
10	Overall	rmse	41.12	49.82	40.47	38.75

MASE

The following table shows the performance measured using MASE across levels for each reconciliation method.

evaluation.query('metric == "mase"')

	level	metric	Base	BottomUp	MinTrace(mint_shrink)	MinTrace(ols)
1	Total	mase	1.59	3.16	2.06	1.67
3	Purpose	mase	1.32	2.28	1.48	1.25
5	State	mase	1.39	1.90	1.40	1.25
7	Regions	mase	1.12	1.19	1.01	0.99
9	Bottom	mase	0.98	0.98	0.94	1.01
11	Overall	mase	1.02	1.06	0.97	1.02

Comparison with fable

Observe that we can recover the results reported by the Forecasting: Principles and Practice. The original results were calculated using the R package fable.

References

• 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.
• Rob Hyndman, Alan Lee, Earo Wang, Shanika Wickramasuriya, and Maintainer Earo Wang (2021). “hts: Hierarchical and Grouped Time Series”. URL https://CRAN.R-project.org/package=hts. R package version 0.3.1.
• Mitchell O’Hara-Wild, Rob Hyndman, Earo Wang, Gabriel Caceres, Tim-Gunnar Hensel, and Timothy Hyndman (2021). “fable: Forecasting Models for Tidy Time Series”. URL https://CRAN.R-project.org/package=fable. R package version 6.0.2.