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. We demonstrate our proposed method by forecasting Australian tourism demand where the data are disaggregated by purpose of travel and geographical region.
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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
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.:
- 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.
- 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.
- 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.
- 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, 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.
- 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.
- 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.
- 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.
- Hubrich, Kirstin, 2003. "Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?," Working Paper Series 0247, European Central Bank.
- 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.
- Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
- Zellner, Arnold & Tobias, Justin, 2004.
"A Note on Aggregation, Disaggregation and Forecasting Performance,"
Staff General Research Papers
12371, Iowa State University, Department of 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.
- 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.
- Solomou, Solomos & Weale, Martin, 1991. "Balanced estimates of UK GDP 1870-1913," Explorations in Economic History, Elsevier, vol. 28(1), pages 54-63, January.
- Richard Stone & D. G. Champernowne & J. E. Meade, 1942. "The Precision of National Income Estimates," Review of Economic Studies, Oxford University Press, vol. 9(2), pages 111-125.
- 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.
- repec:jss:jstsof:27:i03 is not listed on IDEAS
- E. Shlifer & R. W. Wolff, 1979. "Aggregation and Proration in Forecasting," Management Science, INFORMS, vol. 25(6), pages 594-603, June.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2579-2589. 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: (Zhang, Lei)
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.