Decision Trees for Forecasting Trended Demand



In this chapter, we review method selection protocols for three of the commonly used exponential smoothing methods. In addition to protocols which have been previously established, we introduce a new protocol, based on serial variation curves, and a modification of a protocol suggested by Gardner and McKenzie. We also introduce two new decision trees, based on the new protocols, to provide simple ways of choosing between exponential smoothing methods for no trend, damped trend and linear trend. Operational rules are determined for the new rules, determined by detailed experimentation on simulated data. We test the new protocols on real data, and compare the results with established protocols and universal application of smoothing methods. The results show the new approaches to be promising, yielding some improvements in forecasting accuracy. In those cases where no improvement was observed, neither was there any deterioration in forecasting accuracy. This confirms that the new rules introduced in this chapter are robust and worthy of consideration for practical service parts applications.


Mean Absolute Percentage Error Forecast Accuracy Smoothing Parameter Forecast Performance Forecast Method 


  1. Adya M, Collopy F, Armstrong JS, Kennedy M (2001) Automatic identification of time series features for rule-based forecasting. Int J Forecast 17:143–157CrossRefGoogle Scholar
  2. Akaike H (1974) A new look at statistical model identification. IEEE Trans Autom Control 19:716–723CrossRefMATHMathSciNetGoogle Scholar
  3. Armstrong JS (2001) Extrapolation. In: Armstrong JS (ed) Principles of forecasting: a handbook for researchers and practitioners. Kluwer, NorwellGoogle Scholar
  4. Assimakopoulos V, Nikolopoulos N (2000) The theta model: a decomposition approach to forecasting. Int J Forecast 16:521–530CrossRefGoogle Scholar
  5. Atanackov N (2004) Trend forecasting by constrained optimisation and method selection protocols. PhD thesis, Buckinghamshire Chilterns University College, Brunel UniversityGoogle Scholar
  6. Billah B, Hyndman RJ, Koehler AB (2005) Empirical information criteria for time series forecasting model selection. J Stat Comput Simul 75:830–840CrossRefMathSciNetGoogle Scholar
  7. Box GE, Jenkins GM (1970) Time series analysis, forecasting and control. Holden-Day, San FranciscoMATHGoogle Scholar
  8. Boylan JE, Syntetos AA (2008) Forecasting for inventory management of service parts. In: Kobbacy KAH, Murthy DNP (eds) Complex system maintenance handbook. Springer, LondonGoogle Scholar
  9. Chatfield C (1988) Apples, oranges and mean square error. Int J Forecast 4:515–518CrossRefGoogle Scholar
  10. Chatfield C (1992) A commentary on error measures. Int J Forecast 8:100–102CrossRefGoogle Scholar
  11. Collopy F, Armstrong S (1992) Rule-based forecasting: Development and validation of an expert systems approach to combining time-series extrapolations. Manage Sci 38:1394–1414CrossRefGoogle Scholar
  12. Commandeur JJF, Koopman SJ (2007) An introduction to state space time series analysis. Oxford University Press, OxfordMATHGoogle Scholar
  13. Durbin J, Watson GS (1951) Testing for serial correlation in least squares regression. Biometrika 38:159–177MATHMathSciNetGoogle Scholar
  14. Fildes R (1992) The evaluation of extrapolative forecasting methods. Int J Forecast 8:81–98CrossRefGoogle Scholar
  15. Fildes R, Hibon M, Makridakis S, Meade N (1998) Generalising about univariate forecasting methods. Int J Forecast 14:339–358CrossRefGoogle Scholar
  16. Fortuin L (1980) The all-time requirements of spare parts for service after sales–theoretical analysis and practical results. Int J Oper Prod Manage 1:59–69CrossRefGoogle Scholar
  17. Gardner ES Jr (1999) Note: rule-based forecasting vs damped trend exponential smoothing. Manage Sci 45:1169–1176CrossRefGoogle Scholar
  18. Gardner ES Jr (2006) Exponential smoothing: the state of the art, Part II. Int J Forecast 22:637–666CrossRefGoogle Scholar
  19. Gardner ES Jr, McKenzie E (1985) Forecasting trends in time series. Manage Sci 31:1237–1246CrossRefMATHGoogle Scholar
  20. Gardner ES Jr, McKenzie E (1988) Model identification in exponential smoothing. J Oper Res Soc 39:863–867CrossRefGoogle Scholar
  21. Goodrich RL (1990) Applied statistical forecasting. Business Forecast Systems, Inc, BelmontGoogle Scholar
  22. Goodrich RL (2001) Commercial software in the M3-competition. Int J Forecast 17:560–565Google Scholar
  23. Hannan EJ, Quinn BG (1979) The determination of the order of an autoregression. J R Stat Soc Ser B 41:190–195MATHMathSciNetGoogle Scholar
  24. Harrison PJ (1967) Exponential smoothing and short-term sales forecasting. Manage Sci 13:821–842CrossRefGoogle Scholar
  25. Harvey AC (1984) A unified view of statistical forecasting procedures. J Forecast 3:245–283CrossRefGoogle Scholar
  26. Harvey AC (2006) Forecasting with unobserved components time series models. In: Elliott G, Granger CWJ, Timmermann A (eds) Handbook of economic forecasting, vol 1. Elsevier, AmsterdamGoogle Scholar
  27. Holt CC (1957) Forecasting seasonals and trends by exponentially weighted moving averages. ONR memorandum, 52. Carnegie Institute of Technology, Pittsburgh, PAGoogle Scholar
  28. Holt CC (2004a) Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast 20:5–10CrossRefGoogle Scholar
  29. Holt CC (2004b) Author’s retrospective on ‘Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast 20:11–13CrossRefGoogle Scholar
  30. Hurvich CM, Tsai CL (1989) Regression and time series model selection in small samples. Biometrika 76:297–307CrossRefMATHMathSciNetGoogle Scholar
  31. Hyndman RJ, Billah B (2003) Unmasking the Theta method. Int J Forecast 19:287–290CrossRefGoogle Scholar
  32. Hyndman RJ, Koehler AB, Ord JK, Snyder RD (2008) Forecasting with exponential smoothing. the state space approach. Springer, BerlinCrossRefMATHGoogle Scholar
  33. Makridakis S, Hibon M (2000) The M3-competition: results, conclusions and practical concerns. Int J Forecast 16:451–476CrossRefGoogle Scholar
  34. Makridakis S, Wheelright SC, Hyndman RJ (1998) Forecasting: methods and applications, 3rd edn. Wiley, New YorkGoogle Scholar
  35. Makridakis S, Assimakopoulos V, Pagourtzi E, Bougioukos N, Petropoulos F, Nikolopoulos K (2008) PYTHIA: an expert forecasting support system. In: Paper presented at the 28th international symposium on forecasting, Nice, FranceGoogle Scholar
  36. Meade N (2000) Evidence for the selection of forecasting methods. J Forecast 19:515–535CrossRefGoogle Scholar
  37. Newbold P, Granger CWJ (1974) Experience with forecasting univariate time series and the combination of forecasts. J Roy Stat Soc A, Series A 137:131–165CrossRefMathSciNetGoogle Scholar
  38. Pegels CC (1969) Exponential forecasting: some new variations. Manage Sci 12:311–315Google Scholar
  39. Roberts SA (1982) A general class of Holt–Winters type forecasting models. Manage Sci 28:808–820CrossRefMATHGoogle Scholar
  40. Sanders N (1997) Measuring forecasts accuracy: some practical suggestions. Prod Invent Manage J (First Quarter), pp 43–46Google Scholar
  41. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefMATHGoogle Scholar
  42. Shah C (1997) Model selection in univariate time series forecasting using discriminant analysis. Int J Forecast 13:489–500CrossRefGoogle Scholar
  43. Tashman L (2000) Out-of-sample tests of forecasting accuracy: an analysis and review. Int J Forecast 16:437–450CrossRefGoogle Scholar
  44. Tashman LJ, Kruk JM (1996) The use of protocols to select exponential smoothing procedures: a reconsideration of forecasting competitions. Int J Forecast 12:235–253CrossRefGoogle Scholar
  45. Taylor JW (2003) Exponential smoothing with a damped multiplicative trend. Int J Forecast 19:715–725CrossRefGoogle Scholar
  46. Theil H, Wage S (1964) Some observations on adaptive forecasting. Manage Sci 2:189–206Google Scholar
  47. Vokurka RJ, Flores BE, Pearce SL (1996) Automatic feature identification and graphical support in rule-based forecasting: a comparison. Int J Forecast 12:495–512CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Belgrade UniversityBelgradeSerbia
  2. 2.Buckinghamshire New UniversityHigh WycombeUK

Personalised recommendations