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.
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- 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.
- Weale, Martin, 1985. "Testing Linear Hypotheses on National Account Data," The Review of Economics and Statistics, MIT Press, vol. 67(4), pages 685-689, November.
- Hyndman, Rob J. & Khandakar, Yeasmin, 2008.
"Automatic Time Series Forecasting: The forecast Package for R,"
Journal of Statistical Software,
Foundation for Open Access Statistics, 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.
- 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, February.
- 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.
- 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.
- 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.
- Albacete, Rebeca & Senra, Eva & Espasa, Antoni, 2001. "Forecasting inflation in the european monetary union: a disaggregated approach by countries and by sectors," DES - Working Papers. Statistics and Econometrics. WS ws013723, Universidad Carlos III de Madrid. Departamento de Estadística.
- Tobias, Justin & Zellner, Arnold, 2000. "A Note on Aggregation, Disaggregation and Forecasting Performance," Staff General Research Papers Archive 12024, Iowa State University, Department of Economics.
- Zellner, Arnold & Tobias, Justin, 2004. "A Note on Aggregation, Disaggregation and Forecasting Performance," Staff General Research Papers Archive 12371, Iowa State University, Department of Economics.
- 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.
- 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, "undated". "Macroeconomic Forecasting in the Euro Area: Country Specific versus Area-Wide Information," Working Papers 201, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- 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.
- 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.
- Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
- Fair, Ray C & Shiller, Robert J, 1990. "Comparing Information in Forecasts from Econometric Models," American Economic Review, American Economic Association, vol. 80(3), pages 375-389, June.
- 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.
- 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.
- 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 247, European Central Bank.
- 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.
- 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 409-420, November. Full references (including those not matched with items on IDEAS)
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