×

Integrated hierarchical forecasting. (English) Zbl 1431.62436

Summary: Forecasts are often made at various levels of aggregation of individual products, which combine into groups at higher hierarchical levels. We provide an alternative to the traditional discussion of bottom-up versus top-down forecasting by examining how the hierarchy of products can be exploited when forecasts are generated. Instead of selecting series from parts of the hierarchy for forecasting, we explore the possibility of using all the series. Moreover, instead of using the hierarchy after the initial forecasts are generated, we consider the hierarchical structure as a defining feature of the data-generating process and use it to instantaneously generate forecasts for all levels of the hierarchy. This integrated approach uses a state space model and the Kalman filter to explicitly incorporate product dependencies, such as complementarity of products and product substitution, which are otherwise ignored. An empirical study shows the substantial gain in forecast and inventory performance of generalizing the bottom-up and top-down forecast approaches to an integrated approach. The integrated approach is applicable to hierarchical forecasting in general, and extends beyond the current application of demand forecasting for manufacturers.

MSC:

62M20 Inference from stochastic processes and prediction
91B42 Consumer behavior, demand theory

Software:

expsmooth
Full Text: DOI

References:

[1] Athanasopoulos, G.; Ahmed, R. A.; Hyndman, R. J., Hierarchical forecasts for Australian domestic tourism, International Journal of Forecasting, 25, 1, 146-166 (2009)
[2] Byron, R. P., The estimation of large social account matrices, Journal of the Royal Statistical Society. Series A (General), 141, 3, 359 (1978) · Zbl 0444.62120
[3] Chen, H.; Boylan, J. E., The effect of correlation between demands on hierarchical forecasting, Advances in business and management forecasting, 6, 173-188 (2009), Emerald Group Publishing Limited
[4] Dangerfield, B. J.; Morris, J. S., Top-down or bottom-up: aggregate versus disaggregate extrapolations, International Journal of Forecasting, 8, 2, 233-241 (1992)
[5] De Gooijer, J. G.; Hyndman, R. J., 25 years of time series forecasting, International Journal of Forecasting, 22, 3, 443-473 (2006)
[6] Durbin, J.; Koopman, S. J., Time series analysis by state space methods (2012), Oxford University Press · Zbl 1270.62120
[7] Edwards, J. B.; Orcutt, G. H., Should aggregation prior to estimation be the rule?, The Review of Economics and Statistics, 51, 4, 409-420 (1969)
[8] Fildes, R.; Nikolopoulos, K.; Crone, S. F.; Syntetos, A. A., Forecasting and operational research: a review, Journal of the Operational Research Society, 59, 9, 1150-1172 (2008) · Zbl 1153.90009
[9] Fliedner, E. B.; Mabert, V. A., Constrained forecasting: some implementation guidelines, Decision Sciences, 23, 5, 1143 (1992)
[10] Fliedner, G., An investigation of aggregate variable time series forecast strategies with specific subaggregate time series statistical correlation, Computers & Operations Research, 26, 10, 1133-1149 (1999) · Zbl 0940.90004
[11] Fliedner, G., Hierarchical forecasting: issues and use guidelines, Industrial Management & Data Systems, 101, 1, 5-12 (2001)
[12] Gardner, E. S.; McKenzie, E., Forecasting trends in time series, Management Science, 31, 10, 1237-1246 (1985) · Zbl 0617.62105
[13] Gordon, T. P.; Morris, J. S.; Dangerfield, B. J., Top-down or bottom-up: which is the best approach to forecasting?, The Journal of Business Forecasting Methods & Systems, 16, 3, 13-16 (1997)
[14] Gross, C. W.; Sohl, J. E., Disaggregation methods to expedite product line forecasting, Journal of Forecasting, 9, 3, 233-254 (1990)
[15] Harvey, A. C., Forecasting, structural time series models and the Kalman filter (1989), Cambridge University Press
[16] Hyndman, R. J.; Ahmed, R. A.; Athanasopoulos, G.; Shang, H. L., Optimal combination forecasts for hierarchical time series, Computational Statistics & Data Analysis, 55, 9, 2579-2589 (2011) · Zbl 1464.62095
[17] Hyndman, R. J.; Koehler, A. B.; Ord, J. K.; Snyder, R. D., Forecasting with exponential smoothing: the state space approach (2008), Springer Science & Business Media · Zbl 1211.62165
[18] Hyndman, R. J.; Lee, A. J.; Wang, E., Fast computation of reconciled forecasts for hierarchical and grouped time series, Computational Statistics & Data Analysis, 97, 16-32 (2016) · Zbl 1468.62086
[19] Kahn, K. B., Revisiting top-down versus bottom-up forecasting, The Journal of Business Forecasting Methods & Systems, 17, 2, 14-19 (1998)
[20] Kohn, R., When is an aggregate of a time series efficiently forecast by its past?, Journal of Econometrics, 18, 3, 337-349 (1982) · Zbl 0487.62083
[21] Lütkepohl, H., Linear transformations of vector ARMA processes, Journal of Econometrics, 26, 3, 283-293 (1984) · Zbl 0555.62072
[22] Moon, S.; Hicks, C.; Simpson, A., The development of a hierarchical forecasting method for predicting spare parts demand in the South Korean navy, International Journal of Production Economics, 140, 2, 794-802 (2012)
[23] Orcutt, G. H.; Watts, H. W.; Edwards, J. B., Data aggregation and information loss, The American Economic Review, 773-787 (1968)
[24] Proietti, T., Comparing seasonal components for structural time series models, International Journal of Forecasting, 16, 2, 247-260 (2000)
[25] Rostami-Tabar, B.; Babai, M. Z.; Ducq, Y.; Syntetos, A. A., Non-stationary demand forecasting by cross-sectional aggregation, International Journal of Production Economics, 170, 297-309 (2015)
[26] Schwarzkopf, A. B.; Tersine, R. J.; Morris, J. S., Top-down versus bottom-up forecasting strategies, The International Journal of Production Research, 26, 11, 1833-1843 (1988)
[27] Snyder, R. D.; Ord, J. K.; Beaumont, A., Forecasting the intermittent demand for slow-moving inventories: a modelling approach, International Journal of Forecasting, 28, 2, 485-496 (2012)
[28] Sohn, S. Y.; Lim, M., Hierarchical forecasting based on AR-GARCH model in a coherent structure, European Journal of Operational Research, 176, 2, 1033-1040 (2007) · Zbl 1109.90321
[29] Solomou, S.; Weale, M., Balanced estimates of UK GDP 1870-1913, Explorations in Economic History, 28, 1, 54-63 (1991)
[30] Solomou, S.; Weale, M., Balanced estimates of national accounts when measurement errors are autocorrelated: the UK, 1920-38, Journal of the Royal Statistical Society. Series A (Statistics in Society), 156, 1, 89 (1993)
[31] Solomou, S.; Weale, M., UK national income, 1920-1938: the implications of balanced estimates, The Economic History Review, 49, 1, 101-115 (1996)
[32] Stone, R.; Champernowne, D. G.; Meade, J. E., The precision of national income estimates, The Review of Economic Studies, 9, 2, 111 (1942)
[33] Syntetos, A. A.; Babai, Z.; Boylan, J. E.; Kolassa, S.; Nikolopoulos, K., Supply chain forecasting: theory, practice, their gap and the future, European Journal of Operational Research, 252, 1, 1-26 (2016) · Zbl 1346.90181
[34] Syntetos, A. A.; Boylan, J. E.; Disney, S. M., Forecasting for inventory planning: a 50-year review, Journal of the Operational Research Society, 60, 1, S149-S160 (2009) · Zbl 1168.90305
[35] Tiao, G. C.; Guttman, I., Forecasting contemporal aggregates of multiple time series, Journal of Econometrics, 12, 2, 219-230 (1980) · Zbl 0435.62099
[36] Weale, M., Testing linear hypothesis on national account data, The Review of Economics and Statistics, 67, 4, 685 (1985)
[37] Weale, M., The reconciliation of values, volumes and prices in the national accounts, Journal of the Royal Statistical Society. Series A (Statistics in Society), 151, 1, 211 (1988)
[38] Wei, W. W.S.; Abraham, B., Forecasting contemporal time series aggregates, Communications in Statistics - Theory and Methods, 10, 13, 1335-1344 (1981) · Zbl 0464.62089
[39] Widiarta, H.; Viswanathan, S.; Piplani, R., On the effectiveness of top-down strategy for forecasting autoregressive demands, Naval Research Logistics, 54, 2, 176-188 (2007) · Zbl 1126.62088
[40] Widiarta, H.; Viswanathan, S.; Piplani, R., Forecasting aggregate demand: an analytical evaluation of top-down versus bottom-up forecasting in a production planning framework, International Journal of Production Economics, 118, 1, 87-94 (2009)
[41] Zellner, A., On the aggregation problem: a new approach to a troublesome problem, (Fox, K. A.; Sengupta, J. K.; Narasimham, G. V.L., Economic Models, Estimation and Risk Programming (1969), Springer), 365-374 · Zbl 0263.90007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.