Probabilistic forecast reconciliation: Properties, evaluation and score optimisation.
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| Title: | Probabilistic forecast reconciliation: Properties, evaluation and score optimisation. |
|---|---|
| Authors: | Panagiotelis, Anastasios1 (AUTHOR) anastasios.panagiotelis@sydney.edu.au, Gamakumara, Puwasala2 (AUTHOR) puwasala.gamakumara@gmail.com, Athanasopoulos, George1,3 (AUTHOR) george.athanasopoulos@monash.edu, Hyndman, Rob J.2 (AUTHOR) rob.hyndman@monash.edu |
| Source: | European Journal of Operational Research. Apr2023, Vol. 306 Issue 2, p693-706. 14p. |
| Subjects: | Time series analysis, Forecasting, Variograms |
| Abstract: | • Forecast reconciliation in the probabilistic setting is rigorously developed. Point forecast reconciliation is extended in a novel way to the probabilistic setting. • Results are derived for the Gaussian and non-Gaussian case. • Theorems on scoring rules are derived with recommendations for forecast evaluation. • A new reconciliation method based on score optimisation and stochastic gradient descent is proposed. • The new methods are shown to improve forecast accuracy in a simulated and empirical setting. We develop a framework for forecasting multivariate data that follow known linear constraints. This is particularly common in forecasting where some variables are aggregates of others, commonly referred to as hierarchical time series, but also arises in other prediction settings. For point forecasting, an increasingly popular technique is reconciliation, whereby forecasts are made for all series (so-called base forecasts) and subsequently adjusted to cohere with the constraints. We extend reconciliation from point forecasting to probabilistic forecasting. A novel definition of reconciliation is developed and used to construct densities and draw samples from a reconciled probabilistic forecast. In the elliptical case, we prove that true predictive distributions can be recovered using reconciliation even when the location and scale of base predictions are chosen arbitrarily. Reconciliation weights are estimated to optimise energy or variogram score. The log score is not considered since it is improper when comparing unreconciled to reconciled forecasts, a result also proved in this paper. Due to randomness in the objective function, optimisation uses stochastic gradient descent. This method improves upon base forecasts in simulated and empirical data, particularly when the base forecasting models are severely misspecified. For milder misspecification, extending popular reconciliation methods for point forecasting results in similar performance to score optimisation. [ABSTRACT FROM AUTHOR] |
| Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 161080769 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Probabilistic forecast reconciliation: Properties, evaluation and score optimisation. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Panagiotelis%2C+Anastasios%22">Panagiotelis, Anastasios</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> anastasios.panagiotelis@sydney.edu.au</i><br /><searchLink fieldCode="AR" term="%22Gamakumara%2C+Puwasala%22">Gamakumara, Puwasala</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> puwasala.gamakumara@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Athanasopoulos%2C+George%22">Athanasopoulos, George</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> george.athanasopoulos@monash.edu</i><br /><searchLink fieldCode="AR" term="%22Hyndman%2C+Rob+J%2E%22">Hyndman, Rob J.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> rob.hyndman@monash.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22European+Journal+of+Operational+Research%22">European Journal of Operational Research</searchLink>. Apr2023, Vol. 306 Issue 2, p693-706. 14p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Time+series+analysis%22">Time series analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Forecasting%22">Forecasting</searchLink><br /><searchLink fieldCode="DE" term="%22Variograms%22">Variograms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: • Forecast reconciliation in the probabilistic setting is rigorously developed. Point forecast reconciliation is extended in a novel way to the probabilistic setting. • Results are derived for the Gaussian and non-Gaussian case. • Theorems on scoring rules are derived with recommendations for forecast evaluation. • A new reconciliation method based on score optimisation and stochastic gradient descent is proposed. • The new methods are shown to improve forecast accuracy in a simulated and empirical setting. We develop a framework for forecasting multivariate data that follow known linear constraints. This is particularly common in forecasting where some variables are aggregates of others, commonly referred to as hierarchical time series, but also arises in other prediction settings. For point forecasting, an increasingly popular technique is reconciliation, whereby forecasts are made for all series (so-called base forecasts) and subsequently adjusted to cohere with the constraints. We extend reconciliation from point forecasting to probabilistic forecasting. A novel definition of reconciliation is developed and used to construct densities and draw samples from a reconciled probabilistic forecast. In the elliptical case, we prove that true predictive distributions can be recovered using reconciliation even when the location and scale of base predictions are chosen arbitrarily. Reconciliation weights are estimated to optimise energy or variogram score. The log score is not considered since it is improper when comparing unreconciled to reconciled forecasts, a result also proved in this paper. Due to randomness in the objective function, optimisation uses stochastic gradient descent. This method improves upon base forecasts in simulated and empirical data, particularly when the base forecasting models are severely misspecified. For milder misspecification, extending popular reconciliation methods for point forecasting results in similar performance to score optimisation. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.ejor.2022.07.040 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 693 Subjects: – SubjectFull: Time series analysis Type: general – SubjectFull: Forecasting Type: general – SubjectFull: Variograms Type: general Titles: – TitleFull: Probabilistic forecast reconciliation: Properties, evaluation and score optimisation. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Panagiotelis, Anastasios – PersonEntity: Name: NameFull: Gamakumara, Puwasala – PersonEntity: Name: NameFull: Athanasopoulos, George – PersonEntity: Name: NameFull: Hyndman, Rob J. IsPartOfRelationships: – BibEntity: Dates: – D: 16 M: 04 Text: Apr2023 Type: published Y: 2023 Identifiers: – Type: issn-print Value: 03772217 Numbering: – Type: volume Value: 306 – Type: issue Value: 2 Titles: – TitleFull: European Journal of Operational Research Type: main |
| ResultId | 1 |
