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Macroeconomic Forecasting in the Era of Big Data pp 689–719Cite as

Hierarchical Forecasting

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Part of the book series: Advanced Studies in Theoretical and Applied Econometrics ((ASTA,volume 52))

Abstract

Accurate forecasts of macroeconomic variables are crucial inputs into the decisions of economic agents and policy makers. Exploiting inherent aggregation structures of such variables, we apply forecast reconciliation methods to generate forecasts that are coherent with the aggregation constraints. We generate both point and probabilistic forecasts for the first time in the macroeconomic setting. Using Australian GDP we show that forecast reconciliation not only returns coherent forecasts but also improves the overall forecast accuracy in both point and probabilistic frameworks.

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Notes

  1. 1.

    Strictly speaking \(\mathcal {A}\) is a Borel set.

  2. 2.

    The relevant github repository is https://github.com/PuwasalaG/Hierarchical-Book-Chapter.

  3. 3.

    Breve is used instead of a hat or tilde to denote that this can be the error for either a base or reconciled forecast.

References

  • Amemiya, T., & Wu, R. Y. (1972). The effect of aggregation on prediction in the autoregressive model. Journal of the American Statistical Association, 67(339), 628–632. arXiv: 0026.

    Google Scholar 

  • Andrawis, R. R., Atiya, A. F., & El-Shishiny, H. (2011). Combination of long term and short term forecasts, with application to tourism demand forecasting. International Journal of Forecasting, 27(3), 870–886. https://doi.org/10.1016/j.ijforecast.2010.05.019

    Article  Google Scholar 

  • Athanasopoulos, G., Ahmed, R. A., & Hyndman, R. J. (2009). Hierarchical forecasts for Australian domestic tourism. International Journal of Forecasting, 25(1), 146–166. https://doi.org/10.1016/j.ijforecast.2008.07.004

    Article  Google Scholar 

  • Athanasopoulos, G., Hyndman, R. J., Kourentzes, N., & Petropoulos, F. (2017). Forecasting with temporal hierarchies. European Journal of Operational Research, 262, 60–74.

    Article  Google Scholar 

  • Athanasopoulos, G., Steel, T., & Weatherburn, D. (2019). Forecasting prison numbers: A grouped time series approach. Melbourne: Monash University.

    Google Scholar 

  • Australian Bureau of Statistics. (2015). Australian system of national accounts: Concepts, sources and methods. Cat 5216.0.

    Google Scholar 

  • Australian Bureau of Statistics. (2018). Australian national accounts: National income, expenditure and product. Cat 5206.0.

    Google Scholar 

  • Billio, M., Casarin, R., Ravazzolo, F., & Van Dijk, H. K. (2013). Time-varying combinations of predictive densities using nonlinear filtering. Journal of Econometrics, 177(2), 213–232.

    Article  Google Scholar 

  • Brewer, K. (1973). Some consequences of temporal aggregation and systematic sampling for ARMA and ARMAX models. Journal of Econometrics, 1(2), 133–154. https://doi.org/10.1016/03044076(73)900158

    Article  Google Scholar 

  • Capistrán, C., Constandse, C., & Ramos-Francia, M. (2010). Multi-horizon inflation forecasts using disaggregated data. Economic Modelling, 27(3), 666–677.

    Article  Google Scholar 

  • Carriero, A., Clark, T. E., & Marcellino, M. (2015). Realtime nowcasting with a Bayesian mixed frequency model with stochastic volatility. Journal of the Royal Statistical Society: Series A (Statistics in Society), 178(4), 837–862.

    Article  Google Scholar 

  • Clark, T. E., & Ravazzolo, F. (2015). Macroeconomic forecasting performance under alternative specifications of time-varying volatility. Journal of Applied Econometrics, 30(4), 551–575.

    Article  Google Scholar 

  • Cogley, T., Morozov, S., & Sargent, T. J. (2005). Bayesian fan charts for UK inflation: Forecasting and sources of uncertainty in an evolving monetary system. Journal of Economic Dynamics and Control, 29(11), 1893–1925.

    Article  Google Scholar 

  • Dunn, D. M., Williams, W. H., & Dechaine, T. L. (1976). Aggregate versus subaggregate models in local area forecasting. Journal of American Statistical Association, 71(353), 68–71. https://doi.org/10.2307/2285732

    Article  Google Scholar 

  • Gamakumara, P. (2019). Probabilistic forecasts in hierarchical time series (Doctoral dissertation, Monash University).

    Google Scholar 

  • Gamakumara, P., Panagiotelis, A., Athanasopoulos, G., & Hyndman, R. J. (2018). Probabilistic forecasts in hierarchical time series (Working paper No. 11/18). Monash University Econometrics & Business Statistics.

    Google Scholar 

  • Geweke, J., & Amisano, G. (2010). Comparing and evaluating Bayesian predictive distributions of asset returns. International Journal of Forecasting, 26(2), 216–230.

    Article  Google Scholar 

  • Gneiting, T. (2005). Weather forecasting with ensemble methods. Science, 310(5746), 248–249. https://doi.org/10.1126/science.1115255

    Article  Google Scholar 

  • Gneiting, T., & Katzfuss, M. (2014). Probabilistic forecasting. Annual Review of Statistics and Its Application, 1, 125–151. https://doi.org/10.1146/annurev-statistics-062713-085831

    Article  Google Scholar 

  • Gneiting, T., Stanberry, L. I., Grimit, E. P., Held, L., & Johnson, N. A. (2008). Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds. Test, 17(2), 211–235. https://doi.org/10.1007/s11749-008-0114-x

    Article  Google Scholar 

  • Gross, C. W., & Sohl, J. E. (1990). Disaggregation methods to expedite product line forecasting. Journal of Forecasting, 9(3), 233–254. https://doi.org/10.1002/for.3980090304

    Article  Google Scholar 

  • Hotta, L. K. (1993). The effect of additive outliers on the estimates from aggregated and disaggregated ARIMA models. International Journal of Forecasting, 9(1), 85–93. https://doi.org/10.1016/0169-2070(93)90056-S

    Article  Google Scholar 

  • Hotta, L. K., & Cardoso Neto, J. (1993). The effect of aggregation on prediction in autoregressive integrated moving-average models. Journal of Time Series Analysis, 14(3), 261–269.

    Article  Google Scholar 

  • Hyndman, R. J., Ahmed, R. A., Athanasopoulos, G., & Shang, H. L. (2011). Optimal combination forecasts for hierarchical time series. Computational Statistics and Data Analysis, 55(9), 2579–2589. https://doi.org/10.1016/j.csda.2011.03.006

    Article  Google Scholar 

  • Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and practice. OTexts. Retrieved from https://OTexts.com/fpp2

  • Hyndman, R. J., Athanasopoulos, G., Bergmeir, C., Caceres, G., Chhay, L., O’Hara-Wild, M., … Zhou, Z. (2019). Forecast: Forecasting functions for time series and linear models. Version 8.5. Retrieved from https://CRAN.R-project.org/package=forecast

  • Hyndman, R. J., & Khandakar, Y. (2008). Automatic time series forecasting: The forecast package for R. Journal of Statistical Software, 26(3), 1–22.

    Google Scholar 

  • Hyndman, R. J., Koehler, A. B., Ord, J. K., & Snyder, R. D. (2008). Forecasting with exponential smoothing: The state space approach. Berlin: Springer.

    Book  Google Scholar 

  • Hyndman, R. J., Lee, A. J., & Wang, E. (2016). Fast computation of reconciled forecasts for hierarchical and grouped time series. Computational Statistics and Data Analysis, 97, 16–32. https://doi.org/10.1016/j.csda.2015.11.007

    Article  Google Scholar 

  • Kourentzes, N., Petropoulos, F., & Trapero, J. R. (2014). Improving forecasting by estimating time series structural components across multiple frequencies. International Journal of Forecasting, 30(2), 291–302. https://doi.org/10.1016/j.ijforecast.2013.09.006

    Article  Google Scholar 

  • Manzan, S., & Zerom, D. (2008). A bootstrap-based non-parametric forecast density. International Journal of Forecasting, 24(3), 535–550. https://doi.org/10.1016/j.ijforecast.2007.12.004

    Article  Google Scholar 

  • Marcellino, M. (1999). Some consequences of temporal aggregation in empirical analysis. Journal of Business & Economic Statistics, 17(1), 129–136.

    Google Scholar 

  • Nijman, T. E., & Palm, F. C. (1990). Disaggregate sampling in predictive models. Journal of Business & Economic Statistics, 8(4), 405–415.

    Google Scholar 

  • Panagiotelis, A., Athanasopoulos, G., Hyndman, R. J., Jiang, B., & Vahid, F. (2019). Macroeconomic forecasting for Australia using a large number of predictors. International Journal of Forecasting, 35(2), 616–633.

    Article  Google Scholar 

  • Rossana, R., & Seater, J. (1995). Temporal aggregation and economic times series. Journal of Business & Economic Statistics, 13(4), 441–451.

    Google Scholar 

  • Schäfer, J., & 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), 1–30.

    Article  Google Scholar 

  • Shang, H. L., & Hyndman, R. J. (2017). Grouped functional time series forecasting: An application to age-specific mortality rates. Journal of Computational and Graphical Statistics, 26(2), 330–343. https://doi.org/10.1080/106018600.2016.1237877. arXiv: 1609.04222.

  • Silvestrini, A., Salto, M., Moulin, L., & Veredas, D. (2008). Monitoring and forecasting annual public deficit every month: The case of France. Empirical Economics, 34(3), 493–524. https://doi.org/10.1007/s00181-007-0132-7. arXiv: 0016.

    Article  Google Scholar 

  • Smith, M. S., & Vahey, S. P. (2016). Asymmetric forecast densities for us macroeconomic variables from a Gaussian copula model of cross-sectional and serial dependence. Journal of Business & Economic Statistics, 34(3), 416–434.

    Article  Google Scholar 

  • Ben Taieb, S., Taylor, J. W., & Hyndman, R. J. (2017). Hierarchical probabilistic forecasting of electricity demand with smart meter data (Working paper).

    Google Scholar 

  • Tiao, G. C. (1972). Asymptotic behaviour of temporal aggregates of time series. Biometrika, 59(3), 525–531. arXiv: 0027.

    Google Scholar 

  • Vilar, J. A., & Vilar, J. A. (2013). Time series clustering based on nonparametric multidimensional forecast densities. Electronic Journal of Statistics, 7(1), 1019–1046. https://doi.org/10.1214/13-EJS800

    Article  Google Scholar 

  • Villegas, M. A., & Pedregal, D. J. (2018). Supply chain decision support systems based on a novel hierarchical forecasting approach. Decision Support Systems, 114, 29–36. https://doi.org/10.1016/j.dss.2018.08.003

    Article  Google Scholar 

  • Weiss, C. (2018). Essays in hierarchical time series forecasting and forecast combination (Doctoral dissertation, University of Cambridge).

    Google Scholar 

  • Wickramasuriya, S. L., Athanasopoulos, G., & Hyndman, R. J. (2019). Optimal forecast reconciliation for hierarchical and grouped time series through trace minimization. Journal of the American Statistical Association, 114(526), 804–819. https://doi.org/10.1080/01621459.2018.1448825

    Article  Google Scholar 

  • Yagli, G. M., Yang, D., & Srinivasan, D. (2019). Reconciling solar forecasts: Sequential reconciliation. Solar Energy, 179, 391–397. https://doi.org/10.1016/j.solener.2018.12.075

    Article  Google Scholar 

  • Yang, D., Quan, H., Disfani, V. R., & Liu, L. (2017). Reconciling solar forecasts: Geographical hierarchy. Solar Energy, 146, 276–286. https://doi.org/10.1016/j.solener.2017.02.010

    Article  Google Scholar 

  • Zellner, A., & Montmarquette, C. (1971). A study of some aspects of temporal aggregation problems in econometric analyses. The Review of Economics and Statistics, 53(4), 335–342.

    Article  Google Scholar 

  • Zhang, Y., & Dong, J. (2019). Least squares-based optimal reconciliation method for hierarchical forecasts of wind power generation. IEEE Transactions on Power Systems (forthcoming). https://doi.org/10.1109/TPWRS.2018.2868175

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Author information

Authors and Affiliations

  1. Department of Econometrics and Business Statistics, Monash University, Caulfield, VIC, Australia

    George Athanasopoulos & Anastasios Panagiotelis

  2. Department of Econometrics and Business Statistics, Monash University, Clayton, VIC, Australia

    Puwasala Gamakumara & Rob J. Hyndman

  3. Maldives Monetary Authority (MMA), Malé, Republic of Maldives

    Mohamed Affan

Authors
  1. George Athanasopoulos
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  2. Puwasala Gamakumara
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  3. Anastasios Panagiotelis
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  4. Rob J. Hyndman
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  5. Mohamed Affan
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Corresponding author

Correspondence to George Athanasopoulos .

Editor information

Editors and Affiliations

  1. UHERO and Department of Economics, University of Hawaii at Manoa, Honolulu, HI, USA

    Peter Fuleky

Appendix

Appendix

See Tables 21.1, 21.2, 21.3, 21.4.

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Athanasopoulos, G., Gamakumara, P., Panagiotelis, A., Hyndman, R.J., Affan, M. (2020). Hierarchical Forecasting. In: Fuleky, P. (eds) Macroeconomic Forecasting in the Era of Big Data. Advanced Studies in Theoretical and Applied Econometrics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-030-31150-6_21

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