Forecast Reconciliation

[StatMixedML]

Description

It would be very useful to allow for forecast reconciliation of hierarchical and/or grouped time series. This means that the sum of all forecasts that make up a hierarchy matches to the forecast of the hierarchy. Say, you forecast several time series that are within the same hierarchy + the time series of the total (e.g., all tourism visits in Australia within all territories + Total Tourism of the territories as an aggregate). What forecast reconciliation does it makes sure that the bottom level forecasts match the top-level aggregate forecast. As PyTorch-TS is a probabilistic framework, we also need to make sure that the uncertainty attached to the forecasts are corrected.

Besides cross-sectional hierarchies, you may also want to include temporal hierarchies, so that you train the model on daily, weekly and monthly data, and you make sure that all sum up to the temporal hierarchy of interest, e.g., monthly forecast.

Several paper show that Cross-temporal coherent forecasts improve accuracy compared to not taking the information into account.

References

This is a non-exhaustive list of references intended to give a first overview over the topic:

• https://otexts.com/fpp2/hierarchical.html
• https://robjhyndman.com/publications/coherentprob/
• https://kourentzes.com/forecasting/2019/02/09/towards-the-one-number-forecast/
• https://kourentzes.com/forecasting/wp-content/uploads/2019/02/Kourentzes_2019_Cross_temporal_coherent_forecasts__the_case_of_Australian_tourism_flows.pdf
• https://arxiv.org/pdf/1906.03105.pdf
• https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0223422
• https://arxiv.org/pdf/1906.10586.pdf 👈
• https://arxiv.org/pdf/2006.02043.pdf
• https://arxiv.org/pdf/2006.03373.pdf

[kashif]

awesome suggestions, both of them... let me go through the material you so kindly distilled here and see if we can formulate a plan to tackle them...

[StatMixedML]

Let me know if I can contribute, very happy to.

[StatMixedML]

@kashif Not sure if you had the chance already to go through the material. Very happy to support. Shall we have the discussion on how to proceed offline?

[StatMixedML]

@kashif Based on our discussion about forecast reconciliation, this Paper seems to be good starting point.

[StatMixedML]

Adding the hierarchy of the M5 dataset

[StatMixedML]

That might be of interest also

https://forecasters.org/blog/2020/10/25/call-for-papers-international-journal-of-forecasting-innovations-in-hierarchical-forecasting/