Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911659590680576 |
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| author | Carrara, Chiara Azzimonti, Dario Corani, Giorgio Zambon, Lorenzo |
| author_facet | Carrara, Chiara Azzimonti, Dario Corani, Giorgio Zambon, Lorenzo |
| contents | In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the predictive distribution. To address the problem, we propose a Bayesian reconciliation model that accounts for the uncertainty in the estimation of the covariance matrix. By adopting an Inverse-Wishart prior and assuming Gaussian residuals, the reconciled predictive distribution follows a multivariate t-distribution, obtained in closed-form, rather than a multivariate Gaussian distribution. We evaluate our method on three tourism-related datasets, including a new publicly available dataset. Empirical results show that our approach consistently improves prediction intervals compared to MinT reconciliation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation Carrara, Chiara Azzimonti, Dario Corani, Giorgio Zambon, Lorenzo Methodology Computation In minimum trace (MinT) forecast reconciliation, the covariance matrix of the base forecasts errors plays a crucial role. Typically, this matrix is estimated and then treated as known. This can lead to underestimation of the variance of the predictive distribution. To address the problem, we propose a Bayesian reconciliation model that accounts for the uncertainty in the estimation of the covariance matrix. By adopting an Inverse-Wishart prior and assuming Gaussian residuals, the reconciled predictive distribution follows a multivariate t-distribution, obtained in closed-form, rather than a multivariate Gaussian distribution. We evaluate our method on three tourism-related datasets, including a new publicly available dataset. Empirical results show that our approach consistently improves prediction intervals compared to MinT reconciliation. |
| title | Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2506.19554 |