Optimal combination forecasts for hierarchical time series
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.
|Date of creation:||Jul 2007|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.buseco.monash.edu.au/depts/ebs/Email:
More information through EDIRC
|Order Information:|| Web: http://www.buseco.monash.edu.au/depts/ebs/pubs/wpapers/ Email: |
Please 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.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Solomos Solomou & Martin Weale, 1996. "UK national income, 1920-1938: the implications of balanced estimates," Economic History Review, Economic History Society, vol. 49(1), pages 101-115, 02.
- Solomou, Solomos & Weale, Martin, 1991. "Balanced estimates of UK GDP 1870-1913," Explorations in Economic History, Elsevier, vol. 28(1), pages 54-63, January.
- 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.
- Hubrich, Kirstin, 2003.
"Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?,"
Working Paper Series
0247, 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.
- 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.
- E. Shlifer & R. W. Wolff, 1979. "Aggregation and Proration in Forecasting," Management Science, INFORMS, vol. 25(6), pages 594-603, June.
- 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.
- 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.
- Rob J. Hyndman & Yeasmin Khandakar, .
"Automatic Time Series Forecasting: The forecast Package for R,"
Journal of Statistical Software,
American Statistical Association, vol. 27(i03).
- 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.
- Tiao, G. C. & Guttman, Irwin, 1980. "Forecasting contemporal aggregates of multiple time series," Journal of Econometrics, Elsevier, vol. 12(2), pages 219-230, February.
- 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.
- Massimiliano Marcellino & James H. Stock & Mark W. Watson, .
"Macroeconomic Forecasting in the Euro Area: Country Specific versus Area-Wide Information,"
201, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- 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.
- 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.
- A. Espasa & E. Senra & R. Albacete, 2002. "Forecasting inflation in the European Monetary Union: A disaggregated approach by countries and by sectors," The European Journal of Finance, Taylor & Francis Journals, vol. 8(4), pages 402-421.
- Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2007-9. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simone Grose)
If references are entirely missing, you can add them using this form.