Probabilistic reconciliation of mixed-type hierarchical time series

Lorenzo Zambon, Dario Azzimonti, Nicolò Rubattu, Giorgio Corani
Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, PMLR 244:4078-4095, 2024.

Abstract

Hierarchical time series are collections of time series that are formed via aggregation, and thus adhere to some linear constraints. The forecasts for hierarchical time series should be coherent, i.e., they should satisfy the same constraints. In a probabilistic setting, forecasts are in the form of predictive distributions. Probabilistic reconciliation adjusts the predictive distributions, yielding a joint reconciled distribution that assigns positive probability only to coherent forecasts. There are methods for the reconciliation of hierarchies containing only Gaussian or only discrete predictive distributions; instead, the reconciliation of mixed hierarchies, i.e. mixtures of discrete and continuous time series, is still an open problem. We propose two different approaches to address this problem: mixed conditioning and top-down conditioning. We discuss their properties and we present experiments with datasets containing up to thousands of time series.

Cite this Paper

BibTeX
@InProceedings{pmlr-v244-zambon24a, title = {Probabilistic reconciliation of mixed-type hierarchical time series}, author = {Zambon, Lorenzo and Azzimonti, Dario and Rubattu, Nicol\`o and Corani, Giorgio}, booktitle = {Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence}, pages = {4078--4095}, year = {2024}, editor = {Kiyavash, Negar and Mooij, Joris M.}, volume = {244}, series = {Proceedings of Machine Learning Research}, month = {15--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v244/main/assets/zambon24a/zambon24a.pdf}, url = {https://proceedings.mlr.press/v244/zambon24a.html}, abstract = {Hierarchical time series are collections of time series that are formed via aggregation, and thus adhere to some linear constraints. The forecasts for hierarchical time series should be coherent, i.e., they should satisfy the same constraints. In a probabilistic setting, forecasts are in the form of predictive distributions. Probabilistic reconciliation adjusts the predictive distributions, yielding a joint reconciled distribution that assigns positive probability only to coherent forecasts. There are methods for the reconciliation of hierarchies containing only Gaussian or only discrete predictive distributions; instead, the reconciliation of mixed hierarchies, i.e. mixtures of discrete and continuous time series, is still an open problem. We propose two different approaches to address this problem: mixed conditioning and top-down conditioning. We discuss their properties and we present experiments with datasets containing up to thousands of time series.} }
Endnote
%0 Conference Paper %T Probabilistic reconciliation of mixed-type hierarchical time series %A Lorenzo Zambon %A Dario Azzimonti %A Nicolò Rubattu %A Giorgio Corani %B Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2024 %E Negar Kiyavash %E Joris M. Mooij %F pmlr-v244-zambon24a %I PMLR %P 4078--4095 %U https://proceedings.mlr.press/v244/zambon24a.html %V 244 %X Hierarchical time series are collections of time series that are formed via aggregation, and thus adhere to some linear constraints. The forecasts for hierarchical time series should be coherent, i.e., they should satisfy the same constraints. In a probabilistic setting, forecasts are in the form of predictive distributions. Probabilistic reconciliation adjusts the predictive distributions, yielding a joint reconciled distribution that assigns positive probability only to coherent forecasts. There are methods for the reconciliation of hierarchies containing only Gaussian or only discrete predictive distributions; instead, the reconciliation of mixed hierarchies, i.e. mixtures of discrete and continuous time series, is still an open problem. We propose two different approaches to address this problem: mixed conditioning and top-down conditioning. We discuss their properties and we present experiments with datasets containing up to thousands of time series.
APA
Zambon, L., Azzimonti, D., Rubattu, N. & Corani, G.. (2024). Probabilistic reconciliation of mixed-type hierarchical time series. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 244:4078-4095 Available from https://proceedings.mlr.press/v244/zambon24a.html.

Related Material