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Articles

Probabilistic Forecast Reconciliation under the Gaussian Framework

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References

  • Ben Taieb, S., Huser, R., Hyndman, R. J., and Genton, M. G. (2016), “Forecasting Uncertainty and in Electricity and Smart Meter and Data by Boosting Additive Quantile Regression,” IEEE Transactions on Smart Grid, 7, 2448–2455.
  • Ben Taieb, S., and Koo, B. (2019), “Regularized Regression for Hierarchical Forecasting Without Unbiasedness Conditions,” in The 25th ACMSIGKDD Conference on Knowledge Discovery and Data Mining (KDD ’19), Anchorage, AK, USA.
  • Ben Taieb, S., Taylor, J. W., and Hyndman, R. J. (2020), “Hierarchical Probabilistic Forecasting of Electricity Demand with Smart Meter Data,” Journal of the American Statistical Association, 116, 27–43.
  • Berry, L. R., Helman, P., and West, M. (2020), “Probabilistic Forecasting of Heterogeneous Consumer Transaction-Sales Time Series,” International Journal of Forecasting, 36, 552–569.
  • Bertani, N., Satopää, V. A., and Jensen, S. T. (2020), “Joint Bottom-Up Method for Hierarchical Time-Series: Application to Australian Tourism,” available at SSRN: DOI: 10.2139/ssrn.3542278.
  • Brockwell, P. J., and Davis, R. A. (2016), Introduction to Time Series and Forecasting, New York, NY: Springer.
  • Clement, M. P. (2004), “Evaluating the Bank of England Density Forecasts of Inflation,” The Economic Journal, 114, 844–866.
  • Clement, M. P. (2018), “Are Macroeconomic Density Forecasts Informative?” International Journal of Forecasting, 34, 181–198.
  • Dunn, D. M., Williams, W. H., and DeChaine, T. L. (1976), “Aggregate versus Subaggregate Models in Local Area Forecasting,” Journal of the American Statistical Association, 71, 68–71.
  • Gamakumara, P. (2020), “Probabilistic Forecast Reconciliation: Theory and Applications,” PhD thesis, Monash University.
  • Gneiting, T., Stanberry, L. I., Grimit, E. P., Held, L., and Johnson, N. A. (2008), “Assessing Probabilistic Forecasts of Multivariate Quantities, with an Application to Ensemble Predictions of Surface Winds,” Test, 17, 211–235.
  • Hardin, J., Garcia, S. R., and Golan, D. (2013), “A Method for Generating Realistic Correlation Matrices,” The Annals of Applied Statistics, 7, 1733–1762.
  • Hong, T., Pinson, P., Fan, S., Zareipour, H., Troccoli, A., and Hyndman, R. J. (2016), “Probabilistic Energy Forecasting: Global Energy Forecasting Competition 2014 and Beyond,” International Journal of Forecasting, 32, 896–913.
  • Hyndman, R., Athanasopoulos, G., Bergmeir, C., Caceres, G., Chhay, L., O’Hara-Wild, M., Petropoulos, F., Razbash, S., Wang, E., and Yasmeen, F. (2020), forecast: Forecasting Functions for Time Series and Linear Models, R package version 8.12.
  • Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G., and Shang, H. L. (2011), “Optimal Combination Forecasts for Hierarchical Time Series,” Computational Statistics & Data Analysis, 55, 2579–2589.
  • Hyndman, R. J., and Khandakar, Y. (2008), “Automatic Time Series Forecasting: The Forecast Package for R,” Journal of Statistical Software, 26, 1–22.
  • Hyndman, R. J., Koehler, A. B., Ord, J. K., and Snyder, R. D. (2008), Forecasting with Exponential Smoothing: The State Space Approach, Berlin, Heidelberg: Springer.
  • Hyndman, R. J., Lee, A. J., and Wang, E. (2016), “Fast Computation of Reconciled Forecasts for Hierarchical and Grouped Time Series,” Computational Statistics & Data Analysis, 97, 16–32.
  • Jeon, J., Panagiotelis, A., and Petropoulos, F. (2019), “Probabilistic Forecast Reconciliation with Applications to Wind Power and Electric Load,” European Journal of Operational Research, 279, 364–379.
  • Jeon, J., and Taylor, J. W. (2012), “Using Conditional Kernel Density Estimation for Wind Power Density Forecasting,” Journal of the American Statistical Association, 107, 66–79.
  • Kolassa, S. (2016), “Evaluating Predictive Count Data Distributions in Retail Sales Forecasting,” International Journal of Forecasting, 32, 788–803.
  • Leutbecher, M. (2019), “Ensemble Size: How Suboptimal is Less than Infinity?” Quarterly Journal of the Royal Meteorological Society, 145, 107–128.
  • Leutbecher, M., and Palmer, T. N. (2008), “Ensemble Forecasting,” Journal of Computational Physics, 227, 3515–3539.
  • Liu, L., Moon, H. R., and Schorfheide, F. (2021), “Panel Forecasts of Country-Level Covid-19 Infections,” Journal of Econometrics, 220, 2–22. DOI: 10.1016/j.jeconom.2020.08.010.
  • Lütkepohl, H. (2005), New Introduction to Multiple Time Series Analysis, Berlin, Heidelberg: Springer.
  • Orcutt, G. H., Watts, H. W., and Edwards, J. B. (1968), “Data Aggregation and Information Loss,” The American Economic Review, 58, 773–787.
  • Panagiotelis, A., Athanasopoulos, G., Gamakumara, P., and Hyndman, R. J. (2021), “Forecast Reconciliation: A Geometric View with New Insights on Bias Correction,” International Journal of Forecasting, 37, 343–359.
  • Panagiotelis, A., Gamakumara, P., Athanasopoulos, G., and Hyndman, R. J. (2022), “Probabilistic Forecast Reconciliation: Properties, Evaluation and Score Optimisation,” European Journal of Operational Research, 306, 693–706.
  • Pennings, C. L. P., and van Dalen, J. (2017), “Integrated Hierarchical Forecasting,” European Journal of Operational Research, 263, 412–418.
  • Pinson, P., and Tastu, J. (2013), “Discrimination Ability of the Energy Score,” Technical Report 15, Technical University of Denmark.
  • Rossi, B. (2014), “Density Forecasts in Economics and Policymaking,” Technical Report 37, Centre de Recerca en Economia Internacional.
  • Schäfer, J., and Strimmer, K. (2005), “A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics,” Statistical Applications in Genetics and Molecular Biology, 4, 1–30.
  • Scheuerer, M., and Hamill, T. M. (2015), “Variogram-based Proper Scoring Rules for Probabilistic Forecasts of Multivariate Quantities,” Monthly Weather Review, 143, 1321–1334.
  • Shang, H. L. (2017), “Reconciling Forecasts of Infant Mortality Rates at National and Sub-national Levels: Grouped Time-Series Methods,” Population Research and Policy Review, 36, 55–84.
  • Shlifer, E., and Wolff, R. W. (1979), “Aggregation and Proration in Forecasting,” Management Science, 25, 594–603.
  • Sloughter, J. M., Gneiting, T., and Raftery, A. E. (2013), “Probabilistic Wind Vector Forecasting Using Ensembles and Bayesian Model Averaging,” Monthly Weather Review, 141, 2107–2119.
  • van Erven, T., and Cugliari, J. (2015), “Game-Theorically Optimal Reconciliation of Contemporaneous Hierarchical Time Series Forecasts,” in Modeling and Stochastic Learning for Forecasting in High Dimensions, volume 217 of Lecture notes in Statistics, eds. A. Antoniadis, X. Brossat, and J. M. Poggi, pp. 297–317, Cham: Springer.
  • Wickramasuriya, S. L. (2017), “Optimal Forecasts for Hierarchicaland Grouped Time Series,” PhD thesis, Monash University.
  • Wickramasuriya, S. L. (2021), “Properties of Point Forecast Reconciliation Approaches,” arXiv:2103.11129.
  • Wickramasuriya, S. L., Athanasopoulos, G., and Hyndman, R. J. (2019), “Optimal Forecast Reconciliation for Hierarchical and Grouped Time Series through Trace Minimization,” Journal of the American Statistical Association, 114, 804–819.