bayesRecon-package: bayesRecon: Probabilistic Reconciliation via Conditioning

In bayesRecon: Probabilistic Reconciliation via Conditioning

bayesRecon: Probabilistic Reconciliation via Conditioning

Description

Provides methods for probabilistic reconciliation of hierarchical forecasts of time series. The available methods include analytical Gaussian reconciliation (Corani et al., 2021) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-030-67664-3_13")}, MCMC reconciliation of count time series (Corani et al., 2024) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ijforecast.2023.04.003")}, Bottom-Up Importance Sampling (Zambon et al., 2024) \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11222-023-10343-y")}, methods for the reconciliation of mixed hierarchies (Mix-Cond and TD-cond) (Zambon et al., 2024) https://proceedings.mlr.press/v244/zambon24a.html, analytical reconciliation with Bayesian treatment of the covariance matrix (Carrara et al., 2025) \Sexpr[results=rd]{tools:::Rd_expr_doi(" 10.48550/arXiv.2506.19554")}.

Learn more

To learn more about bayesRecon, start with the vignettes: browseVignettes(package = "bayesRecon")

Reconciliation functions

The package implements reconciliation via conditioning for probabilistic forecasts of hierarchical time series. The main functions are:

• reconc_gaussian(): reconciliation via conditioning, assumes multivariate Gaussian base forecasts; this is done analytically;

• reconc_BUIS(): reconciliation via conditioning of any probabilistic forecast via importance sampling; this is the recommended option for non-Gaussian base forecasts;

• reconc_MCMC(): reconciliation via conditioning of discrete probabilistic forecasts via Markov Chain Monte Carlo;

• reconc_MixCond(): reconciliation via conditioning of mixed hierarchies, where the upper forecasts are multivariate Gaussian and the bottom forecasts are discrete distributions;

• reconc_TDcond(): reconciliation via top-down conditioning of mixed hierarchies, where the upper forecasts are multivariate Gaussian and the bottom forecasts are discrete distributions;

• reconc_t(): reconciliation via conditioning with uncertain covariance matrix; the reconciled forecasts are multivariate Student-t; this is done analytically.

Utility functions

• temporal_aggregation(): temporal aggregation of a given time series object of class ts;

• get_reconc_matrices(): aggregation and summing matrices for a temporal hierarchy of time series from user-selected list of aggregation levels;

• schaferStrimmer_cov(): computes the Schäfer-Strimmer shrinkage estimator for the covariance matrix;

• multi_log_score_optimization(): estimates the optimal degrees of freedom for reconc_t() by maximizing the leave-one-out (LOO) multivariate log density;

• PMF: functions for handling PMF objects (sampling, computing statistics like mean, variance, quantiles, and summaries).

Author(s)

Maintainer: Dario Azzimonti [e-mail] (ORCID)

Authors:

• Lorenzo Zambon [e-mail] (ORCID)

• Stefano Damato [e-mail] (ORCID)

• Nicolò Rubattu [e-mail] (ORCID)

• Giorgio Corani [e-mail] (ORCID)

References

Carrara, C., Corani, G., Azzimonti, D., & Zambon, L. (2025). Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation. arXiv preprint arXiv:2506.19554. https://arxiv.org/abs/2506.19554.

Corani, G., Azzimonti, D., Augusto, J.P.S.C., Zaffalon, M. (2021). Probabilistic Reconciliation of Hierarchical Forecast via Bayes' Rule. ECML PKDD 2020. Lecture Notes in Computer Science, vol 12459. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-3-030-67664-3_13")}.

Corani, G., Azzimonti, D., Rubattu, N. (2024). Probabilistic reconciliation of count time series. International Journal of Forecasting 40 (2), 457-469. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ijforecast.2023.04.003")}.

Zambon, L., Azzimonti, D. & Corani, G. (2024). Efficient probabilistic reconciliation of forecasts for real-valued and count time series. Statistics and Computing 34 (1), 21. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11222-023-10343-y")}.

Zambon, L., Agosto, A., Giudici, P., Corani, G. (2024). Properties of the reconciled distributions for Gaussian and count forecasts. International Journal of Forecasting (in press). \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.ijforecast.2023.12.004")}.

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, PMLR 244:4078-4095. https://proceedings.mlr.press/v244/zambon24a.html.

See Also

Useful links:

• https://github.com/IDSIA/bayesRecon

• https://idsia.github.io/bayesRecon/

• Report bugs at https://github.com/IDSIA/bayesRecon/issues

bayesRecon documentation built on March 8, 2026, 9:08 a.m.