Skip to main content

Decision Trees for Forecasting Trended Demand

  • Chapter
  • First Online:
Service Parts Management

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    A consequence of this choice is that a direct comparison with M3-competition results will not be possible.

  2. 2.

    A drawback of the DW statistic has been taken into account. The Durbin-Watson statistic has a gap between the significant positive autocorrelation, representing the DTM model, and not significant autocorrelation, representing the LGM model. Therefore, if the result belongs to that gap it follows that the DW test is inconclusive. Therefore, an operational rule had to be adopted in order to overcome the problem. There were two possibilities: either to allocate the inconclusive time series to the LGM model or to the DTM model. Having analysed the above issue in both cases during the simulation experiment, it was concluded that the penalty in terms of forecast accuracy is lower, if the inconclusive time series are allocated to the DTM model. Since the LGM model is a special case of the DTM model (for ϕ = 1), it follows that the LGM could be detected, but not vice versa.

References

  • Adya M, Collopy F, Armstrong JS, Kennedy M (2001) Automatic identification of time series features for rule-based forecasting. Int J Forecast 17:143–157

    Article  Google Scholar 

  • Akaike H (1974) A new look at statistical model identification. IEEE Trans Autom Control 19:716–723

    Article  MATH  MathSciNet  Google Scholar 

  • Armstrong JS (2001) Extrapolation. In: Armstrong JS (ed) Principles of forecasting: a handbook for researchers and practitioners. Kluwer, Norwell

    Google Scholar 

  • Assimakopoulos V, Nikolopoulos N (2000) The theta model: a decomposition approach to forecasting. Int J Forecast 16:521–530

    Article  Google Scholar 

  • Atanackov N (2004) Trend forecasting by constrained optimisation and method selection protocols. PhD thesis, Buckinghamshire Chilterns University College, Brunel University

    Google Scholar 

  • Billah B, Hyndman RJ, Koehler AB (2005) Empirical information criteria for time series forecasting model selection. J Stat Comput Simul 75:830–840

    Article  MathSciNet  Google Scholar 

  • Box GE, Jenkins GM (1970) Time series analysis, forecasting and control. Holden-Day, San Francisco

    MATH  Google Scholar 

  • Boylan JE, Syntetos AA (2008) Forecasting for inventory management of service parts. In: Kobbacy KAH, Murthy DNP (eds) Complex system maintenance handbook. Springer, London

    Google Scholar 

  • Chatfield C (1988) Apples, oranges and mean square error. Int J Forecast 4:515–518

    Article  Google Scholar 

  • Chatfield C (1992) A commentary on error measures. Int J Forecast 8:100–102

    Article  Google Scholar 

  • Collopy F, Armstrong S (1992) Rule-based forecasting: Development and validation of an expert systems approach to combining time-series extrapolations. Manage Sci 38:1394–1414

    Article  Google Scholar 

  • Commandeur JJF, Koopman SJ (2007) An introduction to state space time series analysis. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Durbin J, Watson GS (1951) Testing for serial correlation in least squares regression. Biometrika 38:159–177

    MATH  MathSciNet  Google Scholar 

  • Fildes R (1992) The evaluation of extrapolative forecasting methods. Int J Forecast 8:81–98

    Article  Google Scholar 

  • Fildes R, Hibon M, Makridakis S, Meade N (1998) Generalising about univariate forecasting methods. Int J Forecast 14:339–358

    Article  Google Scholar 

  • Fortuin L (1980) The all-time requirements of spare parts for service after sales–theoretical analysis and practical results. Int J Oper Prod Manage 1:59–69

    Article  Google Scholar 

  • Gardner ES Jr (1999) Note: rule-based forecasting vs damped trend exponential smoothing. Manage Sci 45:1169–1176

    Article  Google Scholar 

  • Gardner ES Jr (2006) Exponential smoothing: the state of the art, Part II. Int J Forecast 22:637–666

    Article  Google Scholar 

  • Gardner ES Jr, McKenzie E (1985) Forecasting trends in time series. Manage Sci 31:1237–1246

    Article  MATH  Google Scholar 

  • Gardner ES Jr, McKenzie E (1988) Model identification in exponential smoothing. J Oper Res Soc 39:863–867

    Article  Google Scholar 

  • Goodrich RL (1990) Applied statistical forecasting. Business Forecast Systems, Inc, Belmont

    Google Scholar 

  • Goodrich RL (2001) Commercial software in the M3-competition. Int J Forecast 17:560–565

    Google Scholar 

  • Hannan EJ, Quinn BG (1979) The determination of the order of an autoregression. J R Stat Soc Ser B 41:190–195

    MATH  MathSciNet  Google Scholar 

  • Harrison PJ (1967) Exponential smoothing and short-term sales forecasting. Manage Sci 13:821–842

    Article  Google Scholar 

  • Harvey AC (1984) A unified view of statistical forecasting procedures. J Forecast 3:245–283

    Article  Google Scholar 

  • 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, Amsterdam

    Google Scholar 

  • Holt CC (1957) Forecasting seasonals and trends by exponentially weighted moving averages. ONR memorandum, 52. Carnegie Institute of Technology, Pittsburgh, PA

    Google Scholar 

  • Holt CC (2004a) Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast 20:5–10

    Article  Google Scholar 

  • Holt CC (2004b) Author’s retrospective on ‘Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast 20:11–13

    Article  Google Scholar 

  • Hurvich CM, Tsai CL (1989) Regression and time series model selection in small samples. Biometrika 76:297–307

    Article  MATH  MathSciNet  Google Scholar 

  • Hyndman RJ, Billah B (2003) Unmasking the Theta method. Int J Forecast 19:287–290

    Article  Google Scholar 

  • Hyndman RJ, Koehler AB, Ord JK, Snyder RD (2008) Forecasting with exponential smoothing. the state space approach. Springer, Berlin

    Book  MATH  Google Scholar 

  • Makridakis S, Hibon M (2000) The M3-competition: results, conclusions and practical concerns. Int J Forecast 16:451–476

    Article  Google Scholar 

  • Makridakis S, Wheelright SC, Hyndman RJ (1998) Forecasting: methods and applications, 3rd edn. Wiley, New York

    Google Scholar 

  • 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, France

    Google Scholar 

  • Meade N (2000) Evidence for the selection of forecasting methods. J Forecast 19:515–535

    Article  Google Scholar 

  • Newbold P, Granger CWJ (1974) Experience with forecasting univariate time series and the combination of forecasts. J Roy Stat Soc A, Series A 137:131–165

    Article  MathSciNet  Google Scholar 

  • Pegels CC (1969) Exponential forecasting: some new variations. Manage Sci 12:311–315

    Google Scholar 

  • Roberts SA (1982) A general class of Holt–Winters type forecasting models. Manage Sci 28:808–820

    Article  MATH  Google Scholar 

  • Sanders N (1997) Measuring forecasts accuracy: some practical suggestions. Prod Invent Manage J (First Quarter), pp 43–46

    Google Scholar 

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464

    Article  MATH  Google Scholar 

  • Shah C (1997) Model selection in univariate time series forecasting using discriminant analysis. Int J Forecast 13:489–500

    Article  Google Scholar 

  • Tashman L (2000) Out-of-sample tests of forecasting accuracy: an analysis and review. Int J Forecast 16:437–450

    Article  Google Scholar 

  • Tashman LJ, Kruk JM (1996) The use of protocols to select exponential smoothing procedures: a reconsideration of forecasting competitions. Int J Forecast 12:235–253

    Article  Google Scholar 

  • Taylor JW (2003) Exponential smoothing with a damped multiplicative trend. Int J Forecast 19:715–725

    Article  Google Scholar 

  • Theil H, Wage S (1964) Some observations on adaptive forecasting. Manage Sci 2:189–206

    Google Scholar 

  • Vokurka RJ, Flores BE, Pearce SL (1996) Automatic feature identification and graphical support in rule-based forecasting: a comparison. Int J Forecast 12:495–512

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Natasha N. Atanackov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag London Limited

About this chapter

Cite this chapter

Atanackov, N.N., Boylan, J.E. (2011). Decision Trees for Forecasting Trended Demand. In: Altay, N., Litteral, L. (eds) Service Parts Management. Springer, London. https://doi.org/10.1007/978-0-85729-039-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-0-85729-039-7_3

  • Published:

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-038-0

  • Online ISBN: 978-0-85729-039-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics