@misc{carrara2025,
      title={Modeling the uncertainty on the covariance matrix for probabilistic forecast reconciliation}, 
      author={Chiara Carrara and Dario Azzimonti and Giorgio Corani and Lorenzo Zambon},
      year={2025},
      eprint={2506.19554},
      archivePrefix={arXiv},
      primaryClass={stat.ME},
      url={https://arxiv.org/abs/2506.19554}, 
}


   @Manual{mcomp_pkg,
    title = {Mcomp: Data from the M-Competitions},
    author = {Rob Hyndman},
    year = {2018},
    note = {R package version 2.8},
    url = {https://CRAN.R-project.org/package=Mcomp},
  }
  
  @Article{pkg_forecast,
    title = {Automatic time series forecasting: the forecast package for {R}},
    author = {Rob J Hyndman and Yeasmin Khandakar},
    journal = {Journal of Statistical Software},
    volume = {26},
    number = {3},
    pages = {1--22},
    year = {2008},
    doi = {10.18637/jss.v027.i03},
  }




@article{athanasopoulos2017forecasting,
  title = {Forecasting with temporal hierarchies},
  journal = {European Journal of Operational Research},
  volume = {262},
  number = {1},
  pages = {60-74},
  year = {2017},
  issn = {0377-2217},
  author = {George Athanasopoulos and Rob J. Hyndman and Nikolaos Kourentzes and Fotios Petropoulos}
}

@Manual{hts_pkg,
    title = {hts: Hierarchical and Grouped Time Series},
    author = {Rob Hyndman and Alan Lee and Earo Wang and Shanika Wickramasuriya},
    year = {2021},
    note = {R package version 6.0.2},
    url = {https://CRAN.R-project.org/package=hts},
  }
  
 @Manual{expsmooth_pkg,
    title = {expsmooth: Data Sets from "Forecasting with Exponential Smoothing"},
    author = {Rob J Hyndman},
    year = {2015},
    note = {R package version 2.3},
    url = {https://CRAN.R-project.org/package=expsmooth},
  }

@article{wickramasuriya2019optimal,
  author = {Shanika L. Wickramasuriya and George Athanasopoulos and Rob J. Hyndman},
  title = {Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series Through Trace Minimization},
  journal = {Journal of the American Statistical Association},
  volume = {114},
  number = {526},
  pages = {804-819},
  year  = {2019},
  publisher = {Taylor & Francis},
}

@article{schafer2005shrinkage,
  title={A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics},
  author={Sch{\"a}fer, Juliane and Strimmer, Korbinian},
  journal={Statistical applications in genetics and molecular biology},
  volume={4},
  number={1},
  year={2005},
  publisher={De Gruyter}
}

@article{hyndman2011optimal,
  title={Optimal combination forecasts for hierarchical time series},
  author={Hyndman, Rob J and Ahmed, Roman A and Athanasopoulos, George and Shang, Han Lin},
  journal={Computational statistics \& data analysis},
  volume={55},
  number={9},
  pages={2579--2589},
  year={2011},
  publisher={Elsevier}
}

@article{makridakis2000m3,
  title={The M3-Competition: results, conclusions and implications},
  author={Makridakis, Spyros and Hibon, Michele},
  journal={International journal of forecasting},
  volume={16},
  number={4},
  pages={451--476},
  year={2000},
  publisher={Elsevier}
}


@article{panagiotelis2023probabilistic,
  title = {Probabilistic forecast reconciliation: Properties, evaluation and score optimisation},
  journal = {European Journal of Operational Research},
  volume = {306},
  number = {2},
  pages = {693-706},
  year = {2023},
  issn = {0377-2217},
  author = {Anastasios Panagiotelis and Puwasala Gamakumara and George Athanasopoulos and Rob J. Hyndman},
}


@InProceedings{rangapuram2021end,
  title = 	 {End-to-End Learning of Coherent Probabilistic Forecasts for Hierarchical Time Series},
  author =       {Rangapuram, Syama Sundar and Werner, Lucien D and Benidis, Konstantinos and Mercado, Pedro and Gasthaus, Jan and Januschowski, Tim},
  booktitle = 	 {Proceedings of the 38th International Conference on Machine Learning},
  pages = 	 {8832--8843},
  year = 	 {2021},
  editor = 	 {Meila, Marina and Zhang, Tong},
  volume = 	 {139},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {18--24 Jul},
  publisher =    {PMLR}
}


@InProceedings{corani2021probabilistic,
  author="Corani, Giorgio
  and Azzimonti, Dario
  and Augusto, Jo{\~a}o P. S. C.
  and Zaffalon, Marco",
  editor="Hutter, Frank
  and Kersting, Kristian
  and Lijffijt, Jefrey
  and Valera, Isabel",
  title="Probabilistic Reconciliation of Hierarchical Forecast via Bayes' Rule",
  booktitle="Machine Learning and Knowledge Discovery in Databases",
  year="2021",
  publisher="Springer International Publishing",
  pages="211--226",
  doi="10.1007/978-3-030-67664-3_13"
}

@article{zambon2022efficient,
  title={Efficient probabilistic reconciliation of forecasts for real-valued and count time series},
  author={Zambon, Lorenzo and Azzimonti, Dario and Corani, Giorgio},
  journal={Statistics and Computing},
  volume={34},
  number={1},
  pages={21},
  year={2024},
  publisher={Springer},
  doi={10.1007/s11222-023-10343-y}
}



@article{zambon2024properties,
title = {Properties of the reconciled distributions for Gaussian and count forecasts},
journal = {International Journal of Forecasting},
volume = {40},
number = {4},
pages = {1438-1448},
year = {2024},
issn = {0169-2070},
doi = {https://doi.org/10.1016/j.ijforecast.2023.12.004},
url = {https://www.sciencedirect.com/science/article/pii/S016920702300136X},
author = {Lorenzo Zambon and Arianna Agosto and Paolo Giudici and Giorgio Corani},
keywords = {Reconciliation, Hierarchical forecasting, Importance sampling, Intermittent time series, Probabilistic forecasts}
}




@article{corani2023probabilistic,
  title={Probabilistic reconciliation of count time series},
  author={Corani, Giorgio and Azzimonti, Dario and Rubattu, Nicol{\`o}},
  journal={International Journal of Forecasting},
  volume = {40},
    number = {2},
    pages = {457-469},
    year = {2024},
    issn = {0169-2070},
    doi = {https://doi.org/10.1016/j.ijforecast.2023.04.003},
  publisher={Elsevier}
}




@book{hyndman2008forecasting,
  title={Forecasting with exponential smoothing: the state space approach},
  author={Hyndman, Rob and Koehler, Anne B and Ord, J Keith and Snyder, Ralph D},
  year={2008},
  publisher={Springer Science \& Business Media}
}

@article{agosto2022multivariate,
  title={Multivariate Score-Driven Models for Count Time Series To Assess Financial Contagion},
  author={Agosto, Arianna},
  doi = {10.2139/ssrn.4119895},
  year={2022}
}


@InProceedings{zambon2024mixed,
  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}
}



@article{MAKRIDAKIS20221325,
    title = {{The M5 competition: Background, organization, and implementation}},
    journal = {International Journal of Forecasting},
    volume = {38},
    number = {4},
    pages = {1325-1336},
    year = {2022},
    author = {Spyros Makridakis and Evangelos Spiliotis and Vassilios Assimakopoulos},
    keywords = {Forecasting competitions, M competitions, Accuracy, Uncertainty, Time series, Retail sales forecasting},
    doi = {10.1016/j.ijforecast.2021.07.007}
}

@article{svetunkov2023iets,
  title={{iETS: State space model for intermittent demand forecasting}},
  author={Svetunkov, Ivan and Boylan, John E},
  journal={International Journal of Production Economics},
  volume={265},
  pages={109013},
  year={2023},
  publisher={Elsevier},
  doi={10.1016/j.ijpe.2023.109013}
}


@Manual{smooth_pkg,
    title = {smooth: Forecasting Using State Space Models},
    author = {Ivan Svetunkov},
    year = {2023},
    note = {R package version 4.0.0},
    url = {https://cran.r-project.org/package=smooth},
}
