Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
143 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Probabilistic Reconciliation of Count Time Series (2207.09322v4)

Published 19 Jul 2022 in stat.ME and stat.ML

Abstract: Forecast reconciliation is an important research topic. Yet, there is currently neither formal framework nor practical method for the probabilistic reconciliation of count time series. In this paper we propose a definition of coherency and reconciled probabilistic forecast which applies to both real-valued and count variables and a novel method for probabilistic reconciliation. It is based on a generalization of Bayes' rule and it can reconcile both real-value and count variables. When applied to count variables, it yields a reconciled probability mass function. Our experiments with the temporal reconciliation of count variables show a major forecast improvement compared to the probabilistic Gaussian reconciliation.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (34)
  1. Forecasting with temporal hierarchies. European Journal of Operational Research 2017;262(1):60–74.
  2. Stan: A probabilistic programming language. Journal of Statistical Software, Articles 2017;76(1):1–32. URL: https://www.jstatsoft.org/v076/i01.
  3. On the revision of probabilistic beliefs using uncertain evidence. Artificial Intelligence 2005;163(1):67–90.
  4. Probabilistic reconciliation of hierarchical forecast via Bayes’ rule. In: Proc. European Conf. On Machine Learning and Knowledge Discovery in Database ECML/PKDD. volume 3; 2020. p. 211–226.
  5. Darwiche, A.. Modeling and reasoning with Bayesian networks. Cambridge university press, 2009.
  6. Forecast combination-based forecast reconciliation: Insights and extensions. International Journal of Forecasting 2022;doi:https://doi.org/10.1016/j.ijforecast.2022.07.001.
  7. Multisensor data fusion. Springer handbook of robotics 2016;:867–896.
  8. Gneiting, T.. Quantiles as optimal point forecasts. International Journal of forecasting 2011;27(2):197–207.
  9. Understanding forecast reconciliation. European Journal of Operational Research 2021;294(1):149–160.
  10. Hierarchies everywhere–managing & measuring uncertainty in hierarchical time series. arXiv preprint arXiv:220915583 2022;.
  11. Hyndman, R.. Another look at forecast-accuracy metrics for intermittent demand. Foresight: The International Journal of Applied Forecasting 2006;4(4):43–46.
  12. Hyndman, R.J.. expsmooth: Data Sets from ”Forecasting with Exponential Smoothing”, 2015. URL: https://CRAN.R-project.org/package=expsmooth; r package version 2.3.
  13. Optimal combination forecasts for hierarchical time series. Computational Statistics & Data Analysis 2011;55(9):2579 – 2589.
  14. A review of multivariate distributions for count data derived from the Poisson distribution. Wiley Interdisciplinary Reviews: Computational Statistics 2017;9(3).
  15. Probabilistic forecast reconciliation with applications to wind power and electric load. European Journal of Operational Research 2019;279(2):364–379.
  16. Evaluating probabilistic forecasts with scoringRules. Journal of Statistical Software 2019;90(12):1–37.
  17. Kolassa, S.. Evaluating predictive count data distributions in retail sales forecasting. International Journal of Forecasting 2016;32(3):788–803.
  18. Kolassa, S.. Do we want coherent hierarchical forecasts, or minimal mapes or maes?(we won’t get both!). International Journal of Forecasting 2022;doi:https://doi.org/10.1016/j.ijforecast.2022.11.006.
  19. Elucidate structure in intermittent demand series. European Journal of Operational Research 2021;288(1):141–152.
  20. tscount: An R package for analysis of count time series following generalized linear models. Journal of Statistical Software 2017;82(5):1–51.
  21. Martin, O.. Bayesian analysis with Python: introduction to statistical modeling and probabilistic programming using PyMC3 and ArviZ. Packt Publishing Ltd, 2018.
  22. Uncertain evidence in probabilistic models and stochastic simulators. arXiv preprint arXiv:221012236 2022;.
  23. Temporal hierarchies with autocorrelation for load forecasting. European Journal of Operational Research 2020;280(3):876–888.
  24. Pair copula constructions for multivariate Discrete Data. Journal of the American Statistical Association 2012;107(499):1063–1072.
  25. Probabilistic forecast reconciliation: Properties, evaluation and score optimisation. European Journal of Operational Research 2023;306(2):693–706.
  26. Pearl, J.. Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan kaufmann, 1988.
  27. End-to-end learning of coherent probabilistic forecasts for hierarchical time series. In: Proc. 38th Int. Conference on Machine Learning (ICML). 2021. p. 8832–8843.
  28. Probabilistic programming in Python using PyMC3. PeerJ Computer Science 2016;2:e55.
  29. The accuracy of intermittent demand estimates. International Journal of Forecasting 2005;21(2):303–314.
  30. Hierarchical probabilistic forecasting of electricity demand with smart meter data. Journal of the American Statistical Association 2021;116(533):27–43.
  31. Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. Journal of the American Statistical Association 2019;114(526):804–819.
  32. Optimal non-negative forecast reconciliation. Statistics and Computing 2020;30(5):1167–1182.
  33. ZIM: Zero-Inflated Models (ZIM) for Count Time Series with Excess Zeros, 2018. URL: https://CRAN.R-project.org/package=ZIM; r package version 1.1.0.
  34. Efficient probabilistic reconciliation of forecasts for real-valued and count time series. arXiv 2022;doi:10.48550/ARXIV.2210.02286.
Citations (5)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now