Optimal combination forecasts for hierarchical time series
Abstract
In many applications, there are multiple time series that are hierarchically organized and can be aggregated at several different levels in groups based on products, geography or some other features. We call these "hierarchical time series". They are commonly forecast using either a "bottom-up" or a "top-down" method. In this paper we propose a new approach to hierarchical forecasting which provides optimal forecasts that are better than forecasts produced by either a top-down or a bottom-up approach. Our method is based on independently forecasting all series at all levels of the hierarchy and then using a regression model to optimally combine and reconcile these forecasts. The resulting revised forecasts add up appropriately across the hierarchy, are unbiased and have minimum variance amongst all combination forecasts under some simple assumptions. We show in a simulation study that our method performs well compared to the top-down approach and the bottom-up method. It also allows us to construct prediction intervals for the resultant forecasts. Finally, we apply the method to forecasting Australian tourism demand where the data are disaggregated by purpose of visit and geographical region.Download Info
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.Bibliographic Info
Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 9/07.Length: 22 pages
Date of creation: Jul 2007
Date of revision:
Handle: RePEc:msh:ebswps:2007-9
Contact details of provider:
Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Phone: +61-3-9905-2489
Fax: +61-3-9905-5474
Email:
Web page: http://www.buseco.monash.edu.au/depts/ebs/
More information through EDIRC
Order Information:
Email:
Web: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/
Related research
Keywords: Bottom-up forecasting; combining forecasts; GLS regression; hierarchical forecasting; Moore-Penrose inverse; reconciling forecasts; top-down forecasting.;Other versions of this item:
- Hyndman, Rob J. & Ahmed, Roman A. & Athanasopoulos, George & Shang, Han Lin, 2011. "Optimal combination forecasts for hierarchical time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2579-2589, September.
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Longitudinal Data; Spatial Time Series
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-08-08 (All new papers)
- NEP-ECM-2007-08-08 (Econometrics)
- NEP-ETS-2007-08-08 (Econometric Time Series)
- NEP-FOR-2007-08-08 (Forecasting)
References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
- Kohn, Robert, 1982. "When is an aggregate of a time series efficiently forecast by its past?," Journal of Econometrics, Elsevier, vol. 18(3), pages 337-349, April.
- Kirstin Hubrich, 2003.
"Forecasting euro area inflation: does aggregating forecasts by HICP component improve forecast accuracy?,"
Working Paper Series
247, European Central Bank.
- Hubrich, Kirstin, 2005. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," International Journal of Forecasting, Elsevier, vol. 21(1), pages 119-136.
- Kirstin Hubrich, 2004. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," Computing in Economics and Finance 2004 230, Society for Computational Economics.
- Weale, Martin, 1985. "Testing Linear Hypotheses on National Account Data," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 685-89, November.
- Fair, Ray C & Shiller, Robert J, 1990. "Comparing Information in Forecasts from Econometric Models," American Economic Review, American Economic Association, vol. 80(3), pages 375-89, June.
- George Athanasopoulos & Roman A. Ahmed & Rob J. Hyndman, 2007.
"Hierarchical forecasts for Australian domestic tourism,"
Monash Econometrics and Business Statistics Working Papers
12/07, Monash University, Department of Econometrics and Business Statistics, revised Nov 2007.
- Athanasopoulos, George & Ahmed, Roman A. & Hyndman, Rob J., 2009. "Hierarchical forecasts for Australian domestic tourism," International Journal of Forecasting, Elsevier, vol. 25(1), pages 146-166.
- Rob J. Hyndman & Yeasmin Khandakar, 2007.
"Automatic time series forecasting: the forecast package for R,"
Monash Econometrics and Business Statistics Working Papers
6/07, Monash University, Department of Econometrics and Business Statistics.
- Rob J. Hyndman & Yeasmin Khandakar, . "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, American Statistical Association, vol. 27(i03).
- E. Shlifer & R. W. Wolff, 1979. "Aggregation and Proration in Forecasting," Management Science, INFORMS, vol. 25(6), pages 594-603, June.
- Tiao, G. C. & Guttman, Irwin, 1980. "Forecasting contemporal aggregates of multiple time series," Journal of Econometrics, Elsevier, vol. 12(2), pages 219-230, February.
- Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002.
"A state space framework for automatic forecasting using exponential smoothing methods,"
International Journal of Forecasting,
Elsevier, vol. 18(3), pages 439-454.
- Hyndman, R.J. & Koehler, A.B. & Snyder, R.D. & Grose, S., 2000. "A State Space Framework for Automatic Forecasting Using Exponential Smoothing Methods," Monash Econometrics and Business Statistics Working Papers 9/00, Monash University, Department of Econometrics and Business Statistics.
- Tobias, Justin & Zellner, Arnold, 2000.
"A Note on Aggregation, Disaggregation and Forecasting Performance,"
Staff General Research Papers
12024, Iowa State University, Department of Economics.
- Zellner, Arnold & Tobias, Justin, 2004. "A Note on Aggregation, Disaggregation and Forecasting Performance," Staff General Research Papers 12371, Iowa State University, Department of Economics.
- Edwards, John B & Orcutt, Guy H, 1969. "Should Aggregation Prior to Estimation Be the Rule?," The Review of Economics and Statistics, MIT Press, vol. 51(4), pages 409-20, November.
- Dangerfield, Byron J. & Morris, John S., 1992. "Top-down or bottom-up: Aggregate versus disaggregate extrapolations," International Journal of Forecasting, Elsevier, vol. 8(2), pages 233-241, October.
- Solomou, S. & Weale, M., 1992. "UK National Income 1920-1938: The Implications of Balanced Estimates," Cambridge Working Papers in Economics 9221, Faculty of Economics, University of Cambridge.
- Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2003.
"Macroeconomic forecasting in the Euro area: Country specific versus area-wide information,"
European Economic Review,
Elsevier, vol. 47(1), pages 1-18, February.
- Massimiliano Marcellino & James H. Stock & Mark W. Watson, . "Macroeconomic Forecasting in the Euro Area: Country Specific versus Area-Wide Information," Working Papers 201, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- A. Espasa & E. Senra & R. Albacete, 2002. "Forecasting inflation in the European Monetary Union: A disaggregated approach by countries and by sectors," European Journal of Finance, Taylor and Francis Journals, vol. 8(4), pages 402-421.
- Solomou, Solomos & Weale, Martin, 1991. "Balanced estimates of UK GDP 1870-1913," Explorations in Economic History, Elsevier, vol. 28(1), pages 54-63, January.
- Tian, Yongge & Wiens, Douglas P., 2006. "On equality and proportionality of ordinary least squares, weighted least squares and best linear unbiased estimators in the general linear model," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1265-1272, July.
Citations
RePEc Biblio mentions
As found on the RePEc Biblio, the curated bibliography for Economics: Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Capistrán, Carlos & Constandse, Christian & Ramos-Francia, Manuel, 2010. "Multi-horizon inflation forecasts using disaggregated data," Economic Modelling, Elsevier, vol. 27(3), pages 666-677, May.
- Carlos Medel, 2012.
"How Informative are In–Sample Information Criteria to Forecasting? The Case of Chilean GDP,"
Working Papers Central Bank of Chile
657, Central Bank of Chile.
- Medel, Carlos A., 2012. "How informative are in-sample information criteria to forecasting? the case of Chilean GDP," MPRA Paper 35949, University Library of Munich, Germany.
- George Athanasopoulos & Roman A. Ahmed & Rob J. Hyndman, 2007.
"Hierarchical forecasts for Australian domestic tourism,"
Monash Econometrics and Business Statistics Working Papers
12/07, Monash University, Department of Econometrics and Business Statistics, revised Nov 2007.
- Athanasopoulos, George & Ahmed, Roman A. & Hyndman, Rob J., 2009. "Hierarchical forecasts for Australian domestic tourism," International Journal of Forecasting, Elsevier, vol. 25(1), pages 146-166.
- Carlos Capistrán & Christian Constandse & Manuel Ramos Francia, 2009. "Using Seasonal Models to Forecast Short-Run Inflation in Mexico," Working Papers 2009-05, Banco de México.
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2007-9For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simone Grose).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.

