Joint Bottom-up Method for Probabilistic Forecasting of Hierarchical Time Series

Published Online:https://doi.org/10.1287/opre.2022.0113

References

  • Albert JH , Chib S (1993) Bayesian analysis of binary and polychotomous response data. J. Amer. Statist. Assoc. 88(422):669–679.CrossrefGoogle Scholar
  • Athanasopoulos G , Hyndman RJ , Kourentzes N , Petropoulos F (2017) Forecasting with temporal hierarchies. Eur. J. Oper. Res. 262(1):60–74.CrossrefGoogle Scholar
  • Athanasopoulos G , Gamakumara P , Panagiotelis A , Hyndman RJ , Affan M (2020) Hierarchical forecasting. Fuleky P, ed. Macroeconomic Forecasting in the Era of Big Data (Springer, Berlin, Heidelberg), 689–719.CrossrefGoogle Scholar
  • Barnard J , McCulloch R , Meng X-L (2000) Modeling covariance matrices in terms of standard deviations and correlations, with application to shrinkage. Statist. Sinica 10:1281–1311.Google Scholar
  • Cao Z , Li G , Song H (2017) Modelling the interdependence of tourism demand: The global vector autoregressive approach. Ann. Tourism Res. 67:1–13.CrossrefGoogle Scholar
  • Chen Z , Zhao L (2023) Constructing quantiles via forecast errors: Theory and empirical evidence. Preprint, submitted February 27, https://dx.doi.org/10.2139/ssrn.4371538.Google Scholar
  • Choi S , Ruszczyński A , Zhao Y (2011) A multiproduct risk-averse newsvendor with law-invariant coherent measures of risk. Oper. Res. 59(2):346–364.LinkGoogle Scholar
  • Di Fonzo T , Girolimetto D (2021) Forecast combination based forecast reconciliation: Insights and extensions. Preprint, submitted June 10, https://arxiv.org/abs/2106.05653.Google Scholar
  • Dunn D , Williams W , DeChaine T (1976) Aggregate versus subaggregate models in local area forecasting. J. Amer. Statist. Assoc. 71(353):68–71.CrossrefGoogle Scholar
  • Eckert F , Hyndman RJ , Panagiotelis A (2021) Forecasting Swiss exports using Bayesian forecast reconciliation. Eur. J. Oper. Res. 291(2):693–710.CrossrefGoogle Scholar
  • Enders W (1996) RATS Handbook: Handbook for Econometric Time Series (Wiley, New York).Google Scholar
  • Fan J , Lv J (2008) Sure independence screening for ultrahigh dimensional feature space. J. Roy. Statist. Soc. Ser. B (Statist. Methodological) 70(5):849.CrossrefGoogle Scholar
  • Friedman J , Hastie T , Tibshirani R (2001) The Elements of Statistical Learning , vol. 1 (Springer, New York).Google Scholar
  • Gamakumara P , Panagiotelis A , Athanasopoulos G , Hyndman RJ (2018) Probabilistic forecasts in hierarchical time series. Technical report, Department of Econometrics and Business Statistics, Monash University, VIC, Australia.Google Scholar
  • Gelman A , Jakulin A , Pittau MG , Su Y-S (2008) A weakly informative default prior distribution for logistic and other regression models. Ann. Appl. Statist. 2(4):1360–1383.CrossrefGoogle Scholar
  • Geman S , Geman D (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intelligence 6:721–741.CrossrefGoogle Scholar
  • Gijbels I , Herrmann K (2014) On the distribution of sums of random variables with copula-induced dependence. Insurance: Math. Econom. 59:27–44.CrossrefGoogle Scholar
  • Gneiting T (2011) Making and evaluating point forecasts. J. Amer. Statist. Assoc. 106(494):746–762.CrossrefGoogle Scholar
  • Gneiting T , Katzfuss M (2014) Probabilistic forecasting. Annu. Rev. Statist. Appl. 1:125–151.CrossrefGoogle Scholar
  • Gneiting T , Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102(477):359–378.CrossrefGoogle Scholar
  • Hamilton JD (1994) Time Series Analysis (Princeton University Press, Princeton, NJ).CrossrefGoogle Scholar
  • Hilden J , Gerds TA (2014) A note on the evaluation of novel biomarkers: Do not rely on integrated discrimination improvement and net reclassification index. Statist. Medicine 33(19):3405–3414.CrossrefGoogle Scholar
  • Hollyman R , Petropoulos F , Tipping ME (2021) Understanding forecast reconciliation. Eur. J. Oper. Res. 294(1):149–160.CrossrefGoogle Scholar
  • Hyndman R , Khandakar Y (2008) Automatic time series forecasting: The forecast package for R. J. Statist. Software 26(3):1–22.Google Scholar
  • Hyndman RJ , Ahmed RA , Athanasopoulos G , Shang HL (2011) Optimal combination forecasts for hierarchical time series. Comput. Statist. Data Anal. (Oxford) 55(9):2579–2589.CrossrefGoogle Scholar
  • Ishwaran H , Rao JS (2003) Detecting differentially expressed genes in microarrays using Bayesian model selection. J. Amer. Statist. Assoc. 98(462):438–455.CrossrefGoogle Scholar
  • Ishwaran H , Rao JS (2005) Spike and slab variable selection: Frequentist and Bayesian strategies. Ann. Statist. 33(2):730–773.CrossrefGoogle Scholar
  • Ishwaran H , Rao JS (2011) Consistency of spike and slab regression. Statist. Probability Lett. 81(12):1920–1928.CrossrefGoogle Scholar
  • Ishwaran H , Rao JS (2014) Geometry and properties of generalized ridge regression in high dimensions. Contemporary Math. 622:81–93.CrossrefGoogle Scholar
  • Jeon J , Panagiotelis A , Petropoulos F (2019) Probabilistic forecast reconciliation with applications to wind power and electric load. Eur. J. Oper. Res. 279(2):364–379.CrossrefGoogle Scholar
  • Kadiyala KR , Karlsson S (1997) Numerical methods for estimation and inference in Bayesian VAR-models. J. Appl. Econom. 12(2):99–132.CrossrefGoogle Scholar
  • Li H , Tang Q (2019) Analyzing mortality bond indexes via hierarchical forecast reconciliation. ASTIN Bull. 49(3):823–846.CrossrefGoogle Scholar
  • Lipton ZC (2018) The mythos of model interpretability: In machine learning, the concept of interpretability is both important and slippery. Queue 16(3):31–57.CrossrefGoogle Scholar
  • Madsen H (2007) Time Series Analysis (CRC Press, Boca Raton, FL).CrossrefGoogle Scholar
  • Makridakis S , Spiliotis E , Assimakopoulos V (2022) The m5 competition: Background, organization, and implementation. Internat. J. Forecasting 38(4):1325–1336.CrossrefGoogle Scholar
  • Malsiner-Walli G , Wagner H (2018) Comparing spike and slab priors for Bayesian variable selection. Preprint, submitted December 18, https://arxiv.org/abs/1812.07259.Google Scholar
  • Matheson JE , Winkler RL (1976) Scoring rules for continuous probability distributions. Management Sci. 22(10):1087–1096.LinkGoogle Scholar
  • McCullagh P , Nelder JA (1983) Generalized Linear Models (Routledge, London).CrossrefGoogle Scholar
  • Mitchell TJ , Beauchamp JJ (1988) Bayesian variable selection in linear regression. J. Amer. Statist. Assoc. 83(404):1023–1032.CrossrefGoogle Scholar
  • Ni S , Sun D (2005) Bayesian estimates for vector autoregressive models. J. Bus. Econom. Statist. 23(1):105–117.CrossrefGoogle Scholar
  • Novak J , McGarvie S , Garcia BE (2017) A Bayesian model for forecasting hierarchically structured time series. Preprint, submitted November 13, https://arxiv.org/abs/1711.04738.Google Scholar
  • Oliveira JM , Ramos P (2019) Assessing the performance of hierarchical forecasting methods on the retail sector. Entropy 21(4):436.CrossrefGoogle Scholar
  • Osadchiy N , Gaur V , Seshadri S (2016) Systematic risk in supply chain networks. Management Sci. 62(6):1755–1777.LinkGoogle Scholar
  • Pennings CL , van Dalen J (2017) Integrated hierarchical forecasting. Eur. J. Oper. Res. 263(2):412–418.CrossrefGoogle Scholar
  • Ribeiro MT , Singh S , Guestrin C (2016) “Why should I trust you?” Explaining the predictions of any classifier. Proc. 22nd ACM SIGKDD Internat. Conf. Knowledge Discovery Data Mining (Association for Computing Machinery, New York), 1135–1144.Google Scholar
  • Schäfer J , Strimmer K (2005) A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statist. Appl. Genetics Molecular Biology 4(1):1–30.Google Scholar
  • Schweitzer ME , Cachon GP (2000) Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence. Management Sci. 46(3):404–420.LinkGoogle Scholar
  • Sims CA , Zha T (2006) Does monetary policy generate recessions? Macroeconom. Dynamics 10(2):231–272.CrossrefGoogle Scholar
  • Spiliotis E , Makridakis S , Kaltsounis A , Assimakopoulos V (2021) Product sales probabilistic forecasting: An empirical evaluation using the m5 competition data. Internat. J. Production Econom. 240:108237.CrossrefGoogle Scholar
  • Staël von Holstein C-AS (1970) A family of strictly proper scoring rules which are sensitive to distance. J. Appl. Meteorology 9(3):360–364.CrossrefGoogle Scholar
  • Taieb SB, Taylor JW, Hyndman RJ (2017a) Coherent probabilistic forecasts for hierarchical time series. Precup D, Teh Y, eds. Proc. 34th Internat. Conf. Machine Learn., Proceedings of Machine Learning Research (PMLR, New York), 3348–3357.Google Scholar
  • Taieb SB , Taylor JW , Hyndman RJ (2021) Hierarchical probabilistic forecasting of electricity demand with smart meter data. J. Amer. Statist. Assoc. 116(533):27–43.CrossrefGoogle Scholar
  • Taieb SB, Yu J, Barreto M, Rajagopal R (2017b) Regularization in hierarchical time series forecasting with application to electricity smart meter data. Proc. AAAI Conf. Artificial Intelligence 31(1):4474–4480.Google Scholar
  • Tourism Research Australia (2015) Tourism forecasts. Technical report, Australian Government, Canberra, Australia.Google Scholar
  • Vandeput N (2021) Data Science for Supply Chain Forecasting (Walter de Gruyter GmbH & Co, Berlin).CrossrefGoogle Scholar
  • Wickramasuriya SL , Athanasopoulos G , Hyndman RJ (2019) Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. J. Amer. Statist. Assoc. 114(526):804–819.CrossrefGoogle Scholar
  • Winkler RL (1981) Combining probability distributions from dependent information sources. Management Sci. 27(4):479–488.LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.